Question

give algebraic identies​

Answer 1

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Identity I: (a + b)^2 = a^2 + 2ab + b^2

Identity II: (a – b)^2 = a&2 – 2ab + b^2

Identity III: a^2 – b^2= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x^2 + (a + b) x + ab

Identity V: (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

Identity VI: (a + b)&3 = a^3 + b^3 + 3ab (a + b)

Identity VII: (a – b)^3 = a^3 – b^3 – 3ab (a – b)

Identity VIII: a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca)

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Answer 2

Standard Algebraic Identities:

All the standard Algebraic Identities are derived from the Binomial Theorem, which is given as:

(a+b)n=nC0.an.b0+nC1.an−1.b1+……..+nCn−1.a1.bn−1+nCn.a0.bn

Below are some of the Standard Algebraic Identities:

Identity I: (a + b)2 = a2 + 2ab + b2

Identity II: (a – b)2 = a2 – 2ab + b2

Identity III: a2 – b2= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab

Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)

Identity VII: (a – b)3 = a3 – b3 – 3ab (a – b)

Identity VIII: a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)