Question

Simplify (a-b) (a^2+ b^2 -2 a b)- (a+b) (a^2 + b^2+ 2 AB)

Answer 1

(a-b)(a^2+b^2-2ab)-(a+b)(a^2+b^2+2ab)

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

=a^3-3a^2b+3ab^2-b^3-a^3-3a^2b-3ab^2-b^3

=-6a^2b-2b^3

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Answer 2

(a-b)(a^2-2ab+b^2)-(a+b)(a^2+2ab+b^2)

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

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