Question

Factorize (a+b)³+8(a-b)³​

Answer 1

Answer:

(a+b)^3+8(a-b)^3

=(a+b)^3+{2(a-b)}^3

=(a+b)^3+(2a-2b)^3

=(a+b+2a-2b){(a+b)^2-(a+b)(2a-2b)+(2a-2b)^2}

=(3a-b)(a^2+2ab+b^2-2a^2-2ab+2ab+2b^2+4a^2-8ab+4b^2)

=(3a-b) (3a^2+7b^2-6ab)