{"id":10895,"date":"2024-05-25T10:20:00","date_gmt":"2024-05-25T04:50:00","guid":{"rendered":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/%e0%a4%ac%e0%a5%80%e0%a4%9c%e0%a4%97%e0%a4%a3%e0%a4%bf%e0%a4%a4%e0%a5%80%e0%a4%af-%e0%a4%9f%e0%a4%be%e0%a4%87%e0%a4%b2%e0%a5%8d%e0%a4%b8-%e0%a4%95%e0%a5%80-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95\/"},"modified":"2026-05-14T11:26:06","modified_gmt":"2026-05-14T05:56:06","slug":"%e0%a4%ac%e0%a5%80%e0%a4%9c%e0%a4%97%e0%a4%a3%e0%a4%bf%e0%a4%a4%e0%a5%80%e0%a4%af-%e0%a4%9f%e0%a4%be%e0%a4%87%e0%a4%b2%e0%a5%8d%e0%a4%b8-%e0%a4%95%e0%a5%80-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95","status":"publish","type":"post","link":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/%e0%a4%ac%e0%a5%80%e0%a4%9c%e0%a4%97%e0%a4%a3%e0%a4%bf%e0%a4%a4%e0%a5%80%e0%a4%af-%e0%a4%9f%e0%a4%be%e0%a4%87%e0%a4%b2%e0%a5%8d%e0%a4%b8-%e0%a4%95%e0%a5%80-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95\/","title":{"rendered":"\u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094d\u0938 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094d\u0938 \u0926\u093f\u094d\u0935\u093f\u092e\u0940\u092f \u0906\u0927\u093e\u0930-10 \u092c\u094d\u0932\u0949\u0915\u094d\u0938 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0939\u0948\u0902\u0964 \u092f\u0947 \u092b\u094d\u0932\u0948\u091f\u094d\u0938-\u0932\u0949\u0928\u094d\u0917\u094d\u0938-\u092f\u0942\u0928\u093f\u091f\u094d\u0938 (flats-longs-units) \u092f\u093e \u090f\u095e\u090f\u0932\u092f\u0942 (FLU) \u0915\u0947 \u0928\u093e\u092e \u0938\u0947 \u0932\u094b\u0915\u092a\u094d\u0930\u093f\u092f \u0939\u0948\u0902\u0964 \u090f\u091f \u0930\u093e\u0907\u091f \u090f\u0902\u0917\u0932 \u0915\u0947 \u092e\u093e\u0930\u094d\u091a, 2024 \u0905\u0902\u0915 \u092e\u0947\u0902 \u0907\u0928\u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0917\u0908 \u0925\u0940 [5]\u0964 \u0906\u0938\u093e\u0928 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902 \u0915\u0939\u0947\u0902 \u0924\u094b, \u0926\u0938 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 &#8220;x&#8221; \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u093e\u0902\u0915\u093f\u0924 \u0922\u0902\u0917 \u0938\u0947 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0924\u0940\u0928 \u092c\u0941\u0928\u093f\u092f\u093e\u0926\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u0947\u0902 \u092c\u0928\u0924\u0940 \u0939\u0948\u0902 (\u0905\u0928\u0941\u0936\u0902\u0938\u093f\u0924 \u092e\u093e\u092a : x \u2192 2 \u0907\u0902\u091a \u0914\u0930 1 \u2192 2 \u0938\u0947\u092e\u0940) : <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u092c\u0921\u093c\u093e \u0935\u0930\u094d\u0917, \u092f\u093e\u0928\u0940 \u092b\u094d\u0932\u0948\u091f \u092f\u093e 100, \\(x^2\\) \u092c\u0928 \u091c\u093e\u0924\u093e \u0939\u0948 (x \u00d7 x \u092f\u093e 2 \u0907\u0902\u091a \u00d7 2 \u0907\u0902\u091a)<\/li>\n\n\n\n<li>\u0906\u092f\u0924, \u092f\u093e\u0928\u0940 \u0932\u0949\u0928\u094d\u0917 \u092f\u093e 10, \\(x\\) \u092c\u0928 \u091c\u093e\u0924\u093e \u0939\u0948 (x \u00d7 1 \u092f\u093e 2 \u0907\u0902\u091a \u00d7 2 \u0938\u0947\u092e\u0940)<\/li>\n\n\n\n<li>\u091b\u094b\u091f\u093e \u0935\u0930\u094d\u0917, \u092f\u093e\u0928\u0940 \u092f\u0942\u0928\u093f\u091f \u092f\u093e 1 \u0935\u0948\u0938\u093e \u0939\u0940 \u0930\u0939\u0924\u093e \u0939\u0948 (1 \u00d7 1 \u092f\u093e 2 \u0938\u0947\u092e\u0940 \u00d7 2 \u0938\u0947\u092e\u0940)<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"764\" height=\"337\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-1.png\" alt=\"Algebra-tiles-1\" class=\"wp-image-15298\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-1.png 764w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-1-640x282.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-1-360x159.png 360w\" sizes=\"auto, (max-width: 764px) 100vw, 764px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-1<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0932\u0947\u0915\u093f\u0928 \u090f\u0915 \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0928\u094d\u0924\u0930 \u092f\u0939 \u0939\u0948 \u0915\u093f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u0947\u0902 \u0926\u094b (\u0905\u0932\u0917-\u0905\u0932\u0917) \u0930\u0902\u0917\u094b\u0902 \u092e\u0947\u0902 \u0906\u0924\u0940 \u0939\u0948\u0902 \u0924\u093e\u0915\u093f \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0930\u0942\u092a\u094b\u0902, \u092f\u093e\u0928\u0940 \u0915\u093f \\(x\u00b2\\) \u0914\u0930 \\(-x\u00b2\\), \\(x\\) \u0914\u0930 \\(-x\\), 1 \u0914\u0930 -1 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0947, \u091c\u0948\u0938\u093e \u0915\u093f \u091a\u093f\u0924\u094d\u0930-1 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u0906\u092d\u093e\u0938\u0940 [virtual] (\u0914\u0930 \u0911\u0928\u0932\u093e\u0907\u0928) \u0930\u0942\u092a \u092e\u093e\u092a \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 \u0930\u0902\u0917\u094b\u0902 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0924\u0947 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u0938\u092d\u0940 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u090f\u0915 \u0939\u0940 \u0930\u0902\u0917 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0928\u091c\u093c\u0930\u093f\u090f \u0938\u0947 \u0926\u0947\u0916\u0947\u0902 \u0924\u094b, \u092f\u0926\u093f \u0938\u092d\u0940 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u0947\u0902 \u090f\u0915 \u0939\u0940 \u0930\u0902\u0917 \u0915\u0940 \u0939\u0948\u0902, \u0924\u094b \u0938\u092d\u0940 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u0947\u0902 \u092d\u0940 \u090f\u0915 \u0939\u0940 \u0930\u0902\u0917 \u0915\u0940 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u092e\u0948\u0925\u093f\u0917\u094b\u0928 \u092a\u0949\u0932\u0940\u092a\u0948\u0921 (Mathigon Polypad) \u092e\u0947\u0902 \u0906\u092a \u0938\u092d\u0940 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0938\u092e\u093e\u0928 \u0930\u0902\u0917 \u0915\u093e \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 (\u091a\u093f\u0924\u094d\u0930-1)\u0964 \u090f\u0915 \u0914\u0930 \u0935\u093f\u0915\u0932\u094d\u092a \u092f\u0939 \u0939\u0948 \u0915\u093f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0926\u0941\u0924\u0930\u092b\u093c\u093e (double-sided) \u092c\u0928\u093e\u092f\u093e \u091c\u093e\u090f \u0924\u093e\u0915\u093f \u0909\u0928\u0915\u0947 \u090f\u0915 \u0924\u0930\u092b\u093c \u0915\u0940 \u0938\u0924\u0939 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u090f, \u091c\u092c\u0915\u093f \u0926\u0942\u0938\u0930\u0940 \u0938\u0924\u0939 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932 \u0915\u094b\u0964 \u0926\u0941\u0924\u0930\u092b\u093c\u093e \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u0915\u0908 \u092b\u093c\u093e\u092f\u0926\u0947 \u0939\u0948\u0902, \u091c\u0948\u0938\u0947 \u0915\u093f :  <\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u0907\u0928\u094d\u0939\u0947\u0902 \u0910\u0938\u0947 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0921\u093f\u092c\u094d\u092c\u0947 \u0938\u0947 \u0906\u0938\u093e\u0928\u0940-\u0938\u0947 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0915\u0940 \u0905\u0928\u094d\u0926\u0930 \u0915\u0940 \u0938\u0924\u0939 \u092c\u093e\u0939\u0930\u0940 \u0938\u0924\u0939 \u0938\u0947 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \u0905\u0932\u0917 \u0939\u094b\u0964<\/li>\n\n\n\n<li>\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0926\u094b \u0905\u0932\u0917-\u0905\u0932\u0917 \u0938\u0947\u091f \u092c\u0928\u093e\u0928\u0947 \u0915\u0940 \u092c\u091c\u093e\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u090f\u0915 \u0939\u0940 \u0938\u0947\u091f \u092c\u0928\u093e\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0936\u093f\u0915\u094d\u0937\u0923 \u0915\u0947 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0938\u0947 \u0926\u0947\u0916\u0947\u0902, \u0924\u094b \u092f\u0947 \u0915\u093e\u092b\u093c\u0940 \u092a\u094d\u0930\u092d\u093e\u0935\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0915\u093f\u0938\u0940 \u091f\u093e\u0907\u0932 \u0915\u094b \u092a\u0932\u091f\u0928\u0947 \u092f\u093e \u0909\u0932\u091f\u0928\u0947 \u0938\u0947 \u0909\u0938\u0915\u093e \u091a\u093f\u0939\u094d\u0928 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0947 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u092f\u093e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0947 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u092e\u0947\u0902 \u092c\u0926\u0932 \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \u091f\u093e\u0907\u0932 \u0915\u094b \u092a\u0932\u091f\u0928\u093e \u091a\u093f\u0939\u094d\u0928 \u092c\u0926\u0932\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0918\u091f\u093e\u0935 \u0915\u094b \u0938\u092e\u091d\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0939\u0941\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b\u0924\u093e \u0939\u0948\u0964  <\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u091a\u0942\u0901\u0915\u093f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u092e\u0947\u0902 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u0947\u0902 \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 (integers) \u0915\u0940 \u0938\u092e\u091d \u092c\u0939\u0941\u0924 \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948, \u0916\u093c\u093e\u0938\u0915\u0930 \u0907\u0928 \u092c\u093e\u0924\u094b\u0902 \u0915\u0940 :<\/p>\n\n\n\n<ol style=\"list-style-type:upper-alpha\" class=\"wp-block-list upper-alpha\">\n<li>\u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e (zero-pairs) : 1 \u0914\u0930 -1, \\(x\\) \u0914\u0930 \\(-x, x^2\\) \u0914\u0930 \\(-x^2\\) \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u091c\u093c\u0930\u0942\u0930\u0924 \u0915\u0947 \u0939\u093f\u0938\u093e\u092c \u0932\u093e\u092f\u093e \u092f\u093e \u0939\u091f\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0938\u0947 \u0935\u094d\u092f\u0902\u091c\u0915 (expression) \u0928\u0939\u0940\u0902 \u092c\u0926\u0932\u0924\u093e\u0964<\/li>\n\n\n\n<li>\u0915\u093f\u0938\u0940 \u0930\u093e\u0936\u093f \u0915\u094b \u0918\u091f\u093e\u0928\u093e \u0909\u0938 \u0930\u093e\u0936\u093f \u0915\u0947 \u092f\u094b\u091c\u094d\u092f \u092a\u094d\u0930\u0924\u093f\u0932\u094b\u092e (additive inverse) \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u0924\u0941\u0932\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \\(13, -7, 5x\\) \u0914\u0930 \\(-2x^2\\) \u0915\u094b \u0918\u091f\u093e\u0928\u093e \u0915\u094d\u0930\u092e\u0936: \\(-13, 7, -5x\\) \u0914\u0930 \\(2x^2\\) \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u00d7 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u00d7 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0926\u094b\u0928\u094b\u0902 \u0939\u0940 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 <\/li>\n\n\n\n<li>\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u00d7 \u090b\u0923\u093e\u0924\u094d\u092e\u0915, \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u0924\u0940\u0928 \u092e\u093e\u092a\u094b\u0902 \u0915\u0940 \u0907\u0928 6 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u091c\u093c\u0930\u093f\u090f \u0939\u092e (i) \u090f\u0915 \u091a\u0930 (variable) \u0935\u093e\u0932\u0947 (ii) 2 \u0915\u0940 \u0918\u093e\u0924 (degree) \u0935\u093e\u0932\u0947 (iii) \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0917\u0941\u0923\u093e\u0902\u0915\u094b\u0902 (integer coefficients) \u0935\u093e\u0932\u0947 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092c\u0939\u0941\u092a\u0926 (polynomial) \u0915\u094b \u0926\u0930\u094d\u0936\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u091a\u093f\u0924\u094d\u0930-2 \u092e\u0947\u0902 \u0910\u0938\u0947 \u0915\u0908 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u0939\u093e\u0901 \u0928\u0940\u0932\u093e \u0930\u0902\u0917 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0914\u0930 \u0917\u0941\u0932\u093e\u092c\u0940 \u0930\u0902\u0917 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0907\u0902\u0917\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0927\u094d\u092f\u093e\u0928 \u0926\u0940\u091c\u093f\u090f \u0915\u093f \\((4 \u2013 x^2)\\) \u0905\u0938\u0932 \u092e\u0947\u0902 \\(4 + (-x^{2} )\\) \u0914\u0930 \\(5x\u20131\\) \u0926\u0930\u0905\u0938\u0932 \\(5x+(-1)\\) \u0939\u0948\u0964 \u0907\u0938\u0940\u0932\u093f\u090f \u0939\u092e\u0947\u0902 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0940 \u091c\u093c\u0930\u0942\u0930\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964       <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"898\" height=\"425\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-2.png\" alt=\"Algebra-tiles-2\" class=\"wp-image-15302\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-2.png 898w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-2-640x303.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-2-360x170.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-2-768x363.png 768w\" sizes=\"auto, (max-width: 898px) 100vw, 898px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-2<\/figcaption><\/figure>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-text-align-left mb-0 wp-block-paragraph\">\u0905\u0932\u092c\u0924\u094d\u0924\u093e, \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0938\u0947 \u092d\u093f\u0928\u094d\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0928\u0939\u0940\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f \u092e\u0948\u0925\u093f\u0917\u0949\u0928 \u092a\u0949\u0932\u0940\u092a\u0948\u0921 \u092e\u0947\u0902 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0906\u0927\u093e \u0915\u0930\u0915\u0947 \\(x\/4, x^2\/2, 1\/8\\) \u0906\u0926\u093f \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0932\u0947\u0915\u093f\u0928 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0915\u0947\u0935\u0932 \u0906\u0927\u093e (\u0906\u0921\u093c\u0947 \u092f\u093e \u0916\u0921\u093c\u0947 \u092e\u0947\u0902) \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \\(x\/3, x^2\/5, 1\/6\\) \u0906\u0926\u093f \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u093e \u0938\u092e\u094d\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930-3)\u0964  <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"337\" height=\"579\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-3.png\" alt=\"Algebra-tiles-3\" class=\"wp-image-15305\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-3.png 337w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-3-210x360.png 210w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-3-118x202.png 118w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-3<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">FLU \u0914\u0930 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u090f\u0915 \u0914\u0930 \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0928\u094d\u0924\u0930 \u092f\u0939 \u0939\u0948 \u0915\u093f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u092e\u0947\u0902 \u0932\u0947\u0928-\u0926\u0947\u0928 \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e\u0964 FLU \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902, \u092f\u0939 \u090f\u0915 \u091c\u093e\u0928\u093e-\u092e\u093e\u0928\u093e \u0924\u0925\u094d\u092f \u0939\u0948 \u0915\u093f 10 \u0907\u0915\u093e\u0907\u092f\u093e\u0901 \u092e\u093f\u0932\u0915\u0930 \u090f\u0915 \u0932\u0949\u0928\u094d\u0917 \u092c\u0928\u093e\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 10 \u0932\u0949\u0928\u094d\u0917\u094d\u0938 \u092e\u093f\u0932\u0915\u0930 \u090f\u0915 \u092b\u094d\u0932\u0948\u091f \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902, \u091a\u0942\u0901\u0915\u093f x \u090f\u0915 \u0905\u091c\u094d\u091e\u093e\u0924 \u0930\u093e\u0936\u093f \u0939\u0948 \u092f\u093e \u0907\u0938\u0915\u0947 \u0915\u0908 \u092e\u093e\u0928 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0939\u092e \u0928\u0939\u0940\u0902 \u091c\u093e\u0928\u0924\u0947 \u0915\u093f \u0915\u093f\u0924\u0928\u0947 1 \u092e\u093f\u0932\u0915\u0930 x \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902\u0964 \u0907\u0938\u0932\u093f\u090f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u093f\u0938\u0940 \u0924\u0930\u0939 \u0915\u093e \u0932\u0947\u0928-\u0926\u0947\u0928 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e\u0964 \u092f\u0939 \u0910\u0938\u093e \u0939\u0940 \u0939\u0948 \u091c\u0948\u0938\u0947 \u0915\u093f \u0915\u093f\u0938\u0940 \u092c\u0939\u0941\u092a\u0926 \u0915\u0947 \u092a\u0926\u094b\u0902 \u0915\u094b \u090f\u0915 \u092a\u0926 \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u092c\u0926\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0907\u0938 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0915\u094b \u092a\u0941\u0916\u094d\u093c\u0924\u093e \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092c\u0939\u0941\u092a\u0926\u094b\u0902, \u091c\u0948\u0938\u0947 \u0915\u093f \\(3&#215;2 -2x \u2013 5\\) \u0915\u094b \u0914\u0930 \u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e\u0964     <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u091c\u092c \u0939\u092e \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0941\u091b \u091a\u0940\u091c\u093c\u0947\u0902 \u0905\u092a\u0928\u0947-\u0906\u092a \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948\u0902 :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\((x^2)\\) \u0915\u094b \u2018x \u0915\u093e \u0935\u0930\u094d\u0917\u2019 \u0915\u094d\u092f\u094b\u0902 \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092f\u0939 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0935\u0930\u094d\u0917 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924 \u0939\u0948\u0964<\/li>\n\n\n\n<li>\\((x^2)\\) \u0914\u0930 2x \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0905\u0928\u094d\u0924\u0930\u0964 \u091a\u0942\u0901\u0915\u093f \\((x^2)\\) \u092f\u093e\u0928\u0940 \u0915\u093f \\(x \u00d7 x\\) \u0915\u094b \u090f\u0915 \u0935\u0930\u094d\u0917\u093e\u0915\u093e\u0930 \u091f\u093e\u0907\u0932 \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \\(2x\\) \u092f\u093e\u0928\u0940 \u0915\u093f \\(x + x\\) \u0915\u094b \u0926\u094b \u0906\u092f\u0924\u093e\u0915\u093e\u0930 \u091f\u093e\u0907\u0932\u094b\u0902 \u0938\u0947\u0964<\/li>\n\n\n\n<li>\u0938\u092e\u093e\u0928 \u092a\u0926\u094b\u0902 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u2014 \u090f\u0915 \u0939\u0940 \u092e\u093e\u092a \u0915\u0940 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0917\u093f\u0928\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u092f\u0939\u093e\u0901 \u0924\u0915 \u0915\u093f \u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e\u094b\u0902 (zero pairs) \u0915\u094b \u0939\u091f\u093e\u092f\u093e \u092d\u0940 \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0905\u0932\u0917-\u0905\u0932\u0917 \u092e\u093e\u092a\u094b\u0902 \u0915\u0940 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u092e\u093f\u0932\u093e\u0915\u0930 \u090f\u0915 \u092a\u0926 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0928\u0939\u0940\u0902 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e\u0964<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u091a\u0942\u0901\u0915\u093f \\(x\\) \u0914\u0930 \\(1\\) \u0915\u0947 \u092c\u0940\u091a \u0915\u093e \u0938\u092e\u094d\u092c\u0928\u094d\u0927 \u0905\u091c\u094d\u091e\u093e\u0924 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u091c\u093c\u0930\u093f\u090f \u0926\u094b \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u0915\u094b\u0908 \u0924\u0930\u0940\u0915\u093c\u093e \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u0905\u0932\u092c\u0924\u094d\u0924\u093e, \u0939\u092e \u0926\u094b \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u091c\u094b\u0921\u093c \u092f\u093e \u0918\u091f\u093e\u0935 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u092c\u0936\u0930\u094d\u0924\u0947 \u0915\u093f \u0909\u0928\u094d\u0939\u0947\u0902 \u091f\u093e\u0907\u0932\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u0930\u094d\u0936\u093e\u0928\u093e \u0938\u092e\u094d\u092d\u0935 \u0939\u094b\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1233\" height=\"713\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/08\/fig-4-hi.png\" alt=\"Algebra-tiles-4\" class=\"wp-image-17252\" style=\"object-fit:cover\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/08\/fig-4-hi.png 1233w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/08\/fig-4-hi-623x360.png 623w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/08\/fig-4-hi-349x202.png 349w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/08\/fig-4-hi-768x444.png 768w\" sizes=\"auto, (max-width: 1233px) 100vw, 1233px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-4<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u0928\u093f\u092f\u092e \u0935\u0939\u0940 \u0939\u0948\u0902, \u091c\u094b FLU \u0915\u093e \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0930\u0915\u0947 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u0939\u0948\u0902 :<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092c\u0939\u0941\u092a\u0926 \u0915\u094b \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>\u0938\u092e\u093e\u0928 \u092e\u093e\u092a \u0935\u093e\u0932\u0940 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u092e\u093f\u0932\u093e \u0926\u0947\u0902 \u0914\u0930 \u0936\u0942\u0928\u094d\u092f \u092f\u0941\u0917\u094d\u092e\u094b\u0902 \u0915\u094b \u0939\u091f\u093e \u0926\u0947\u0902\u0964<\/li>\n\n\n\n<li>\u0936\u0947\u0937 \u091f\u093e\u0907\u0932\u0947\u0902 \u092f\u094b\u0917\u092b\u0932 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0902\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0940 \u0924\u0930\u0939 \u0918\u091f\u093e\u0935 \u092f\u093e\u0928\u0940 \\(p(x) \u2013 q(x)\\) \u0915\u0947 \u091a\u0930\u0923 \u0939\u0948\u0902 :<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u092c\u0939\u0941\u092a\u0926 \\(p(x)\\) \u2013 \\(q(x)\\) \u0915\u094b \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>&#8211;\\( q(x)\\) \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \\(q(x)\\) \u0915\u0940 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u092a\u0932\u091f \u0926\u0947\u0902\u0964<\/li>\n\n\n\n<li>\\(p(x)\\) \u0914\u0930 \\(-q(x)\\) \u0915\u094b \u091c\u094b\u0921\u093c\u0947\u0902, \u092f\u093e\u0928\u0940 \u0915\u093f \u0938\u092e\u093e\u0928 \u092e\u093e\u092a \u0915\u0940 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u092e\u093f\u0932\u093e \u0926\u0947\u0902 \u0914\u0930 \u0936\u0942\u0928\u094d\u092f \u092f\u0941\u0917\u094d\u092e\u094b\u0902 \u0915\u094b \u0939\u091f\u093e \u0926\u0947\u0902\u0964<\/li>\n\n\n\n<li>\u0936\u0947\u0937 \u091f\u093e\u0907\u0932\u0947\u0902 \\(p(x) \u2013 q(x) = p(x) + [-q(x)]\\) \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0902\u0964<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/07\/fig-5-hi.png\" alt=\"Algebra-tiles-5\" class=\"wp-image-15311\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-5<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\\(p(x) \u2013 q(x) \\)\u0915\u094b \u090f\u0915 \u0905\u0928\u094d\u092f \u0924\u0930\u0940\u0915\u093c\u0947 \u0938\u0947 \u092d\u0940 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u094b \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 (whole number) \u0915\u0947 \u0932\u093f\u090f \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u093f\u090f \u0917\u090f \u0924\u0930\u0940\u0915\u093c\u0947 \u091c\u0948\u0938\u093e \u0939\u0940 \u0939\u0948 :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/07\/fig-6-hin.png\" alt=\"Algebra-tiles-6\" class=\"wp-image-15314\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-6<\/figcaption><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u092c\u0939\u0941\u092a\u0926 \\(p(x)\\) \u0915\u094b \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0915\u094b\u0908 \u092c\u0939\u0941\u092a\u0926 \\(q(x)\\) \u0939\u0948\u0964<\/li>\n\n\n\n<li>\\(p(x)\\) \u092e\u0947\u0902 \u091c\u093c\u0930\u0942\u0930\u0924 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e \u091c\u094b\u0921\u093c\u0947\u0902 \u0924\u093e\u0915\u093f \\(q(x)\\) \u0915\u094b \u0918\u091f\u093e\u0928\u0947 (\u092f\u093e\u0928\u0940 \u0915\u093f \\(x2, -4x\\) \u0914\u0930 5 \u0915\u094b \u0939\u091f\u093e\u0928\u0947) \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0930\u093e\u0936\u093f \u0939\u094b\u0964<\/li>\n\n\n\n<li>\\(q(x)\\) \u0915\u094b \\(p(x)\\) \u092e\u0947\u0902 \u0938\u0947 \u0918\u091f\u093e\u090f\u0901, \u092f\u093e\u0928\u0940 \u0915\u093f \u090a\u092a\u0930 \u092c\u0924\u093e\u090f \u0924\u0930\u0940\u0915\u093c\u0947 \u0938\u0947 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u0939\u091f\u093e\u090f\u0901\u0964 \u091c\u094b \u092c\u091a\u0924\u093e \u0939\u0948 \u0935\u0939 \\(p(x) \u2013 q(x)\\) \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u091a\u093f\u0924\u094d\u0930-4 \u0926\u094b \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u091c\u094b\u0921\u093c \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u091a\u093f\u0924\u094d\u0930-5 \u0935 6 \u0926\u094b \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u0918\u091f\u093e\u0935 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u092f\u0939 \u0915\u093e\u092b\u093c\u0940 \u0915\u0920\u093f\u0928 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0907\u0938\u092e\u0947\u0902 \u090f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e\u094b\u0902 <span class=\"math mobile-view\">\\((1 \u0914\u0930 -1, x \u0914\u0930 \u2212x, x2 \u0914\u0930 \u2212x2)\\)<\/span> \u0915\u0940 \u091c\u093c\u0930\u0942\u0930\u0924 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e\u0928\u0947 \u090a\u092a\u0930 \u092c\u093f\u0928\u094d\u200d\u0926\u0941 \u0916 \u092e\u0947\u0902 \u092c\u0924\u093e\u092f\u093e \u0925\u093e \u0915\u093f \u0915\u093f\u0938\u0940 \u092a\u0926 \u0915\u094b \u0918\u091f\u093e\u0928\u093e \u0909\u0938\u0915\u0947 \u092f\u094b\u091c\u094d\u092f \u092a\u094d\u0930\u0924\u093f\u0932\u094b\u092e \u0915\u094b \u091c\u094b\u0921\u093c\u0928\u0947 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0918\u091f\u093e\u0935 \u0915\u094b \u090f\u0915 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u091c\u094b\u0921\u093c \u092e\u093e\u0928\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f, \\(q(x)\\) \u0915\u094b \u092a\u0932\u091f\u0928\u093e \u092c\u0939\u0941\u092a\u0926 \u0915\u0947 \u0918\u091f\u093e\u0935 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u093e \u0906\u0938\u093e\u0928 \u0935\u093f\u0915\u0932\u094d\u092a \u0939\u0948\u0964 <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/07\/fig-7-hin.png\" alt=\"Algebra-tiles-7\" class=\"wp-image-15317\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-7<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0917\u0941\u0923\u093e \u0935 \u092d\u093e\u0917 \u0915\u0947 \u0932\u093f\u090f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0905\u0927\u093f\u0915\u0924\u092e 2 \u0915\u0940 \u0918\u093e\u0924 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0939\u0940 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0930\u0915\u0947 \u0926\u094b \u0930\u0948\u0916\u093f\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 (linear polynomials) \u0915\u093e \u0917\u0941\u0923\u0928 2 \u0905\u0902\u0915\u094b\u0902 \u0935\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0917\u0941\u0923\u0928 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091a\u093f\u0924\u094d\u0930-7 \u0915\u0947 \u091a\u0930\u0923 2 \u2018\u0917\u0941\u0923\u0928\u092b\u0932\u2019 \u092e\u0947\u0902 \u092c\u0921\u093c\u0947 \u0914\u0930 \u091b\u094b\u091f\u0947 \u0935\u0930\u094d\u0917\u094b\u0902 \u0914\u0930 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0914\u0930 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u092f\u0924\u094b\u0902 \u0935\u093e\u0932\u0947 \u091a\u093e\u0930 \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u0926\u0947\u0916\u0947\u0902\u0964 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u091a\u0930\u0923 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948\u0902 :   <\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u0917\u0941\u0923\u093e \u0915\u093f\u090f \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u092c\u093e\u090f\u0901 \u0915\u093f\u0928\u093e\u0930\u0947 \u092a\u0930 \u0914\u0930 \u0926\u0942\u0938\u0930\u0947 \u092c\u0939\u0941\u092a\u0926 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u094b \u090a\u092a\u0930\u0940 \u0915\u093f\u0928\u093e\u0930\u0947 \u092a\u0930 \u091c\u092e\u093e\u090f\u0901\u0964<\/li>\n\n\n\n<li>\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091f\u093e\u0907\u0932 \u0915\u0940 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0935\u093f\u092e\u093e (dimension) \u0915\u093e \u0915\u093f\u0928\u093e\u0930\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u092e\u093f\u0932\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0915\u094d\u0930\u092e\u0935\u093f\u0928\u094d\u092f\u093e\u0938 (array) \u0915\u094b \u092d\u0930\u0947\u0902\u0964<\/li>\n\n\n\n<li>\u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e\u094b\u0902 \u0915\u094b \u0939\u091f\u093e \u0926\u0947\u0902 (\u0917\u0941\u0923\u0928\u092b\u0932 \u092e\u0947\u0902 \u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e \u0915\u0939\u093e\u0901 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902? \u091a\u093f\u0924\u094d\u0930-8 \u0926\u0947\u0916\u0947\u0902)\u0964<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u091a\u093f\u0924\u094d\u0930-8 \u0909\u091a\u094d\u091a\u0924\u092e \u0918\u093e\u0924 \u0915\u0947 \u092a\u0926\u094b\u0902 \u0915\u094b \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0930\u0916\u0924\u0947 \u0939\u0941\u090f \u091a\u093f\u0939\u094d\u0928\u094b\u0902 (\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0935 \u090b\u0923\u093e\u0924\u094d\u092e\u0915) \u0915\u0947 \u0938\u0902\u092f\u094b\u091c\u0928\u094b\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u092e\u0947\u0902 \u0907\u0938 \u092c\u093e\u0924 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0928\u094d\u0926\u094d\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f \u091a\u093f\u0939\u094d\u0928 \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u0948\u0938\u0947 \u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0928 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u091c\u093f\u0928\u092e\u0947\u0902 \u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0928 \u091a\u093e\u0930\u094b\u0902 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0938\u092e\u093e\u0928\u0924\u093e\u0913\u0902 \u0914\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928\u0924\u093e\u0913\u0902 \u092a\u0930 \u0917\u093c\u094c\u0930 \u0915\u0930\u0947\u0902\u0964 \u092e\u0927\u094d\u092f \u092a\u0926 \u0915\u0947 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921\u0928 (middle term factorization) \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0938\u092e\u091d\u0928\u093e \u092e\u0939\u0924\u094d\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964 \u0914\u0930 \u0939\u093e\u0901, \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u0947\u0902 \u0907\u0938\u0947 \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0915\u093e\u095e\u0940 \u0905\u091a\u094d\u091b\u0947 \u0938\u0947 \u092e\u0926\u0926 \u0938\u0947 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902!    <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1009\" height=\"548\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-8_11zon.png\" alt=\"Algebra-tiles-8\" class=\"wp-image-15320\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-8_11zon.png 1009w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-8_11zon-640x348.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-8_11zon-360x196.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-8_11zon-768x417.png 768w\" sizes=\"auto, (max-width: 1009px) 100vw, 1009px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-8<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 2 \u0915\u0940 \u0918\u093e\u0924 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092a\u0926 \u092e\u0947\u0902 1 \u0915\u0940 \u0918\u093e\u0924 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092a\u0926 \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0928\u093e (\u091a\u093f\u0924\u094d\u0930-9) FLU \u0915\u0940 \u092e\u0926\u0926 \u0938\u0947 3 \u0905\u0902\u0915\u094b\u0902 \u0935\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 2 \u0905\u0902\u0915\u094b\u0902 \u0935\u093e\u0932\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0928\u0947 \u0938\u0947 \u092d\u0940 \u0915\u093e\u095e\u0940 \u092e\u093f\u0932\u0924\u093e-\u091c\u0941\u0932\u0924\u093e \u0939\u0948\u0964 (\u0926\u0947\u0916\u0947\u0902 \u0938\u0928\u094d\u0926\u0930\u094d\u092d [5]) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u091a\u0930\u0923 1 :<\/strong> \\(x^2\\) \u0915\u0947 \u0932\u093f\u090f \u091f\u093e\u0907\u0932\u0947\u0902 \u0930\u0916\u0947\u0902 \u0914\u0930 \u0906\u0902\u0936\u093f\u0915 \u092d\u093e\u0917\u092b\u0932 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \\(2x\\) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0947\u0902\u0964 \\(x \u0914\u0930 -x\\) \u0915\u0947 \u0924\u0940\u0928 \u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e \u0932\u093e\u090f\u0901 \u0914\u0930 \u0907\u0938 \u091a\u0930\u0923 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0947\u0902\u0964 \u092c\u091a\u0947\u0917\u093e 3x\u22123 (\u091a\u093f\u0924\u094d\u0930-10)\u0964<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u091a\u0930\u0923 2 :<\/strong> \\(x\\) \u091f\u093e\u0907\u0932\u0947\u0902 \u0930\u0916\u0947\u0902 \u0914\u0930 \u092c\u091a\u0947 \u0939\u0941\u090f \u0906\u0902\u0936\u093f\u0915 \u092d\u093e\u0917\u092b\u0932 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 3 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0947\u0902\u0964 1 \u0914\u0930 -1 \u0915\u0947 \u0928\u094c \u0936\u0942\u0928\u094d\u092f-\u092f\u0941\u0917\u094d\u092e \u0932\u093e\u090f\u0901 \u0914\u0930 \u0907\u0938 \u091a\u0930\u0923 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0947\u0902\u0964 \u092f\u0939\u093e\u0901 9 \u0936\u0947\u0937\u092b\u0932 \u0939\u094b\u0917\u093e \u0914\u0930 \\(2x + 3\\) \u092d\u093e\u0917\u092b\u0932 (\u091a\u093f\u0924\u094d\u0930-11)\u0964<br>\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u0905\u0928\u094d\u0924 \u092e\u0947\u0902 \u092d\u093e\u091c\u094d\u092f (dividend) \u0926\u094b \u092d\u093e\u0917\u094b\u0902 \u092e\u0947\u0902 \u0939\u0948\u2013 \u0915\u094d\u0930\u092e\u0935\u093f\u0928\u094d\u092f\u093e\u0938 (array) \u0914\u0930 \u0936\u0947\u0937\u092b\u0932, \u092f\u093e\u0928\u0940 \u0915\u093f<\/p>\n\n\n\n<figure class=\"wp-block-image size-medium\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"133\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-9-640x133.png\" alt=\"Algebra-tiles-9\" class=\"wp-image-15323\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-9-640x133.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-9-360x75.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-9-768x159.png 768w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-tiles-9.png 888w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-9<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/07\/fig-10-hi-1.png\" alt=\"Algebra-tiles-10\" class=\"wp-image-15326\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-10<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u092d\u093e\u091c\u094d\u092f = \u0915\u094d\u0930\u092e\u0935\u093f\u0928\u094d\u092f\u093e\u0938 + \u0936\u0947\u0937\u092b\u0932 = \u092d\u093e\u091c\u0915 \u00d7 \u092d\u093e\u0917\u092b\u0932 + \u0936\u0947\u0937\u092b\u0932, \u0920\u0940\u0915 \u0935\u0948\u0938\u0947 \u0939\u0940 \u091c\u0948\u0938\u0947 \u0915\u093f FLU \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948 (\u091a\u093f\u0924\u094d\u0930-11)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2025\/07\/fig-11-hin.png\" alt=\"Algebra-tiles-11\" class=\"wp-image-15329\"\/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-11<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0938\u092d\u0940 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u0913\u0902 (quadratic identities) \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\((a + b)^ 2\\) \u0914\u0930 \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924<\/li>\n\n\n\n<li>\\((a-b)^ 2\\) \u0914\u0930 \u0938\u092e\u094d\u092c\u0928\u094d\u0927\u093f\u0924<\/li>\n\n\n\n<li>\\((a + b)(a &#8211; b)\\)<\/li>\n\n\n\n<li>\\((a + b)^ 2 + (a &#8211; b)^ 2\\)<\/li>\n\n\n\n<li>\\((a + b)^ 2 &#8211; (a &#8211; b)^ 2\\)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0924\u094b \u091c\u0939\u093e\u0901 \u0924\u0915 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0940 \u092c\u093e\u0924 \u0939\u0948, \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u0947\u0902 \u0907\u0928\u094d\u0939\u0947\u0902 \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0915\u093e\u092b\u093c\u0940 \u092e\u0926\u0926\u0917\u093e\u0930 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f \u092d\u094c\u0924\u093f\u0915 (\u092f\u093e \u0906\u092d\u093e\u0938\u0940) \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u092e\u093e\u092a \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0905\u091a\u094d\u091b\u0940 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940\u0902\u0964 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0930\u0948\u0916\u093f\u0915 \u0935 \u090f\u0915 \u091a\u0930 \u0935\u093e\u0932\u0947 \u0926\u094d\u0935\u093f\u0918\u093e\u0924\u0940\u092f \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0940 \u092a\u0921\u093c\u0924\u093e\u0932 \u0915\u0930\u0928\u093e \u0938\u092e\u094d\u092d\u0935 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092a\u0930 \u0907\u0938\u0915\u0940 \u0917\u0939\u0930\u093e\u0908 \u0938\u0947 \u091b\u093e\u0928-\u092c\u0940\u0928 \u0915\u0930\u0928\u093e \u0905\u092d\u0940 \u092c\u093e\u0915\u093c\u0940 \u0939\u0948\u0964    <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u0915\u0941\u091b \u0938\u0902\u0938\u094d\u0915\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 \u090f\u0915 \u0914\u0930 \u091a\u0930 y \u0935 \u0924\u0940\u0928 \u0914\u0930 \u092e\u093e\u092a \u0915\u0940 \u091f\u093e\u0907\u0932\u0947\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902, \u091c\u0948\u0938\u0947 \u0915\u093f \\(y^2, xy\\) \u0914\u0930 \\(y\\) (\u091a\u093f\u0924\u094d\u0930-12)\u0964 \u0907\u0928\u0938\u0947 \u0926\u094b \u091a\u0930 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0918\u093e\u0924 \u0914\u0930 \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0940 \u0938\u0940\u092e\u093e\u090f\u0901 \u092a\u0939\u0932\u0947 \u0939\u0940 \u0915\u0940 \u0924\u0930\u0939 \u092c\u0928\u0940 \u0930\u0939\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1280\" height=\"652\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-titles-12.png\" alt=\"Algebra-titles-12\" class=\"wp-image-16389\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-titles-12.png 1280w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-titles-12-640x326.png 640w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-titles-12-360x183.png 360w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/05\/Algebra-titles-12-768x391.png 768w\" sizes=\"auto, (max-width: 1280px) 100vw, 1280px\" \/><figcaption class=\"wp-element-caption\">\u091a\u093f\u0924\u094d\u0930-12<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0905\u092d\u0940 \u0924\u0915 \u0939\u092e \u092f\u0939 \u0928\u0939\u0940\u0902 \u091c\u093e\u0901\u091a \u092a\u093e\u090f \u0939\u0948\u0902 \u0915\u093f \u0915\u094d\u092f\u093e \u092f\u0947 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u0947\u0902, \u0935\u093f\u0936\u0947\u0937\u0915\u0930 \\(x\\) \u0914\u0930 1 \u0915\u0947 \u0938\u093e\u0925 \\(y\\), \u0926\u094b \u091a\u0930\u094b\u0902 \u0935\u093e\u0932\u0947 \u0930\u0948\u0916\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u092f\u0941\u0917\u094d\u092e (simultaneous linear equations) \u0915\u094b \u0938\u092e\u091d\u093e\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964<br>3 \u0915\u0940 \u0918\u093e\u0924 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u094b \u0918\u0928\u093e\u092d\u094b\u0902 (cuboids) \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0932\u0947\u0915\u093f\u0928 \u092f\u0939 \u0915\u093e\u092b\u093c\u0940 \u092e\u0941\u0936\u094d\u0915\u093f\u0932 \u0939\u094b\u0917\u093e \u0914\u0930 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0918\u0928\u093e\u092d\u094b\u0902 \u0915\u0947 \u0926\u094b \u0938\u0947\u091f \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0917\u0940\u2013 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u2013\u0915\u094d\u092f\u094b\u0902\u0915\u093f 3-\u0935\u093f\u092e\u093e\u0913\u0902 \u0935\u093e\u0932\u0940 \u091a\u0940\u091c\u093c\u094b\u0902 \u092e\u0947\u0902 \u2018\u092a\u0932\u091f\u0928\u0947\u2019 \u0915\u093e \u092b\u093c\u093e\u092f\u0926\u093e \u0928\u0939\u0940\u0902 \u092e\u093f\u0932 \u092a\u093e\u0924\u093e\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0918\u0928\u093e\u092d \u0936\u093f\u0915\u094d\u0937\u0923-\u0938\u092e\u094d\u092c\u0928\u094d\u0927\u0940 \u0910\u0938\u093e \u0915\u094b\u0908 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0932\u093e\u092d \u092a\u094d\u0930\u0926\u093e\u0928 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u0947, \u091c\u094b \u0907\u0938 \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u094b \u0909\u091a\u093f\u0924 \u0920\u0939\u0930\u093e\u090f\u0964  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0905\u0928\u094d\u0924\u093f\u092e \u092c\u093e\u0924, \u092f\u0926\u093f \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 FLU \u0938\u0947 \u092a\u0930\u093f\u091a\u093f\u0924 \u0928 \u0939\u094b\u0902 \u0924\u094b \u092d\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0938\u0947 \u0909\u0928\u0915\u093e \u092a\u0930\u093f\u091a\u092f \u0915\u0930\u093e\u0928\u093e \u092c\u093f\u0932\u0915\u0941\u0932 \u0920\u0940\u0915 \u0939\u0948\u0964 \u092f\u0947 \u091f\u093e\u0907\u0932\u0947\u0902 FLU \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 \u0939\u0948\u0902 \u0914\u0930 FLU \u0915\u0947 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0947 \u092c\u093e\u0926 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092f\u0939 \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092e\u0939\u091c\u093c &#8217;10 \u0915\u0947 \u0906\u0927\u093e\u093e\u0930 \u0935\u093e\u0932\u0947 \u092c\u0939\u0941\u092a\u0926&#8217; \u0939\u0948\u0902, \u091c\u093f\u0928\u0915\u0947 \u0905\u0902\u0915 \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0932\u0947\u0915\u093f\u0928 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0938\u0947 \u092a\u0939\u0932\u0947 FLU \u0938\u0947 \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u094b\u0928\u093e \u0915\u094b\u0908 \u095b\u0930\u0942\u0930\u0940 \u0936\u0930\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0930\u0902\u0917\u0940\u0928 \u0915\u093e\u0909\u0902\u091f\u0930\u094b\u0902 \u0915\u0947 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0938\u0947 \u0935\u093e\u0915\u093c\u093f\u092b\u093c \u0939\u094b\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 (\u0926\u0947\u0916\u0947\u0902 \u0938\u0928\u094d\u0926\u0930\u094d\u092d [6])\u0964   <\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u091f\u093e\u0907\u0932\u094d\u0938 \u0926\u093f\u094d\u0935\u093f\u092e\u0940\u092f \u0906\u0927\u093e\u0930-10 \u092c\u094d\u0932\u0949\u0915\u094d\u0938 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0939\u0948\u0902\u0964 \u092f\u0947 \u092b\u094d\u0932\u0948\u091f\u094d\u0938-\u0932\u0949\u0928\u094d\u0917\u094d\u0938-\u092f\u0942\u0928\u093f\u091f\u094d\u0938 (flats-longs-units) \u092f\u093e \u090f\u095e\u090f\u0932\u092f\u0942 (FLU) \u0915\u0947 \u0928\u093e\u092e \u0938\u0947 \u0932\u094b\u0915\u092a\u094d\u0930\u093f\u092f \u0939\u0948\u0902\u0964 \u090f\u091f \u0930\u093e\u0907\u091f \u090f\u0902\u0917\u0932 \u0915\u0947 \u092e\u093e\u0930\u094d\u091a, 2024 \u0905\u0902\u0915 \u092e\u0947\u0902 \u0907\u0928\u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0917\u0908 \u0925\u0940 [5]\u0964 \u0906\u0938\u093e\u0928 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902 \u0915\u0939\u0947\u0902 \u0924\u094b, \u0926\u0938 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 &#8220;x&#8221; \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u093e\u0902\u0915\u093f\u0924 \u0922\u0902\u0917 \u0938\u0947 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0924\u0940\u0928 \u092c\u0941\u0928\u093f\u092f\u093e\u0926\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f 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