{"id":949,"date":"2026-10-05T03:21:24","date_gmt":"2026-10-05T03:21:24","guid":{"rendered":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/?p=949"},"modified":"2026-10-05T03:34:37","modified_gmt":"2026-10-05T03:34:37","slug":"4-exploration-of-algebraic-identities","status":"publish","type":"post","link":"https:\/\/academic.pargaidefenceacademy.in\/Class-9th\/2026\/10\/05\/4-exploration-of-algebraic-identities\/","title":{"rendered":"*4* | \u092c\u0940\u091c\u0940\u092f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u0913\u0902 \u0915\u093e \u0905\u0928\u094d\u0935\u0947\u0937\u0923 | Exploration of Algebraic Identities"},"content":{"rendered":"
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Ch4 - \u092c\u0940\u091c\u0940\u092f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e\u0913\u0902 \u0915\u093e \u0905\u0928\u094d\u0935\u0947\u0937\u0923 - \u092d\u093e\u0917 1\/4 - \u092a\u0930\u093f\u091a\u092f<\/span><\/div>\n\n
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\ud83d\udd34 \u092d\u093e\u0917 1\/4 - \u092a\u0930\u093f\u091a\u092f - \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u0915\u094d\u092f\u093e?<\/div>
\u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u0915\u094d\u092f\u093e? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 x \u0915\u0947 \u0915\u0941\u091b \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u092e\u0947\u0902 x \u0915\u0947 \u0938\u092d\u0940 \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964
\u0938\u092e\u0940\u0915\u0930\u0923 : 2x+3=7 \u0938\u093f\u0930\u094d\u092b x=2 \u092a\u0930 \u0938\u0924\u094d\u092f<\/div>
\u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e : (x+1)\u00b2=x\u00b2+2x+1 \u0938\u092d\u0940 x \u092a\u0930 \u0938\u0924\u094d\u092f<\/div><\/div>\u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u0939\u092e\u0947\u0936\u093e \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u092d\u0940 \u0915\u092d\u0940 \u0938\u0924\u094d\u092f\u0964
\u092c\u0940\u091c\u0940\u092f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u0915\u094d\u092f\u094b\u0902? - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>\u0917\u0941\u0923\u093e \u0915\u094b \u091c\u0932\u094d\u0926\u0940 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u092c\u0928\u093e\u0908 \u0917\u0908\u0964 \u092c\u0921\u093c\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0917\u0941\u0923\u093e \u0938\u0942\u0924\u094d\u0930 \u0938\u0947 \u0924\u0947\u091c\u093c \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 1001\u00b2 = (1000+1)\u00b2 = 1000000+2000+1=1002001\u0964 \u092c\u093f\u0928\u093e \u0917\u0941\u0923\u093e \u0915\u0947\u0964
1001\u00b2 = (1000+1)\u00b2 = 1002001 \u0924\u0947\u091c\u093c<\/span>
\u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e = \u0924\u0947\u091c\u093c \u0917\u0923\u0928\u093e<\/span><\/div><\/div><\/div>\n\n
\ud83d\udd35 \u092d\u093e\u0917 2\/4 - \u0935\u0930\u094d\u0917 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e (a+b)\u00b2 (a-b)\u00b2<\/div>
(a+b)\u00b2 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>(a+b)\u00b2 = (a+b)(a+b) = a\u00b2+ab+ba+b\u00b2 = a\u00b2+2ab+b\u00b2
(a+b)\u00b2 = a\u00b2+2ab+b\u00b2<\/div>
\u092a\u0939\u0932\u0947 \u0915\u093e \u0935\u0930\u094d\u0917 +2\u00d7\u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0917\u0941\u0923\u093e+\u0926\u0942\u0938\u0930\u0947 \u0915\u093e \u0935\u0930\u094d\u0917<\/div>
(x+2)\u00b2=x\u00b2+4x+4<\/div>
(101)\u00b2=(100+1)\u00b2=10000+200+1=10201<\/div><\/div>
(a-b)\u00b2 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>(a-b)\u00b2 = a\u00b2-2ab+b\u00b2\u0964 \u092c\u0940\u091a \u092e\u0947\u0902 \u090b\u0923 \u0939\u094b\u0924\u093e \u0939\u0948\u0964
(a-b)\u00b2 = a\u00b2-2ab+b\u00b2<\/div>
(x-3)\u00b2=x\u00b2-6x+9<\/div>
(99)\u00b2=(100-1)\u00b2=10000-200+1=9801<\/div><\/div>\u091a\u093f\u0924\u094d\u0930 \u0938\u0947: \u092c\u0921\u093c\u0947 \u0935\u0930\u094d\u0917 \u0938\u0947 \u0926\u094b \u0906\u092f\u0924 \u0918\u091f\u093e\u0913 \u090f\u0915 \u091b\u094b\u091f\u093e \u091c\u094b\u0921\u093c\u094b\u0964<\/div><\/div>\n\n
\ud83d\udfe2 \u092d\u093e\u0917 3\/4 - (a+b)(a-b) \u0914\u0930 (x+a)(x+b)<\/div>
(a+b)(a-b) \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>(a+b)(a-b)=a\u00b2-ab+ba-b\u00b2=a\u00b2-b\u00b2\u0964 \u092c\u0940\u091a \u0935\u093e\u0932\u093e \u0915\u091f \u091c\u093e\u0924\u093e \u0939\u0948\u0964
(a+b)(a-b)=a\u00b2-b\u00b2<\/div>
\u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u0935\u0930\u094d\u0917 \u0905\u0902\u0924\u0930<\/div>
(x+5)(x-5)=x\u00b2-25<\/div>
101\u00d799=(100+1)(100-1)=10000-1=9999 \u0924\u0947\u091c\u093c<\/div><\/div>
(x+a)(x+b) \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>(x+a)(x+b)=x\u00b2+(a+b)x+ab
(x+a)(x+b)=x\u00b2+(a+b)x+ab<\/div>
(x+2)(x+3)=x\u00b2+5x+6<\/div>
(x+4)(x-2)=x\u00b2+2x-8<\/div><\/div>\u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917\u0940\u0964<\/div><\/div>\n\n
\ud83d\udfe3 \u092d\u093e\u0917 4\/4 - \u0909\u092a\u092f\u094b\u0917 \u0914\u0930 Trick<\/div>
\u0918\u0928 \u0938\u0930\u094d\u0935\u0938\u092e\u093f\u0915\u093e \u092a\u0930\u093f\u091a\u092f - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>(a+b)\u00b3 = a\u00b3+3a\u00b2b+3ab\u00b2+b\u00b3 = a\u00b3+b\u00b3+3ab(a+b)
(a+b)\u00b3=a\u00b3+b\u00b3+3ab(a+b)<\/div>
(a-b)\u00b3=a\u00b3-b\u00b3-3ab(a-b)<\/div>
a\u00b3+b\u00b3=(a+b)(a\u00b2-ab+b\u00b2)<\/div>
a\u00b3-b\u00b3=(a-b)(a\u00b2+ab+b\u00b2)<\/div><\/div>
Trick \u0938\u092d\u0940 \u090f\u0915 \u0938\u093e\u0925 - \u0939\u0947\u0921\u093f\u0902\u0917<\/div>
(a+b)\u00b2=a\u00b2+2ab+b\u00b2<\/div>
(a-b)\u00b2=a\u00b2-2ab+b\u00b2<\/div>
a\u00b2-b\u00b2=(a+b)(a-b)<\/div>
(x+a)(x+b)=x\u00b2+(a+b)x+ab<\/div>
(a+b)\u00b3=a\u00b3+b\u00b3+3ab(a+b)<\/div>
a\u00b3+b\u00b3=(a+b)(a\u00b2-ab+b\u00b2)<\/div>
101\u00b2 99\u00b2 101\u00d799 \u0924\u0947\u091c\u093c<\/div><\/div><\/div><\/div>\n<\/div>\n\n
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