Question

(a+b)^3-8(a-b)^3 I need process​

Answer 1

Answer:

= (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]

= (a+b-2a+2b) [a^2 +b^2 + 2ab + (a+b) (2a-2b) + (2a+2b)^2]

= (3b - a) [a^2 + b^2 + 2ab + 2a^3 - 2ab + 2ab - 2b^2 + (2a-2b)^2]

= (3b - a) [3a^2 + 2ab - b^2 + (2a-2b)^2]

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

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

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

therefore, (a+b)^2 - 8(a+b)^2 = (-a + 3b) (7a^2 - 6ab + 3b^2)