Question

Write all algebraic identities

Answer 1

Answer:

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

Some Standard Algebraic Identities list are given below:

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)

Example 1: Find the product of (x + 1)(x + 1) using standard algebraic identities.

Solution: (x + 1)(x + 1) can be written as (x + 1)2. Thus, it is of the form Identity I where a = x and b = 1. So we have,

(x + 1)2 = (x)2 + 2(x)(1) + (1)2 = x2 + 2x + 1