Question

已知a-b=-2,求a^3+6ab-b^3 要求先化简在求值

Answer 1

a^3+6ab-b^3

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

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

=-2a^2-2ab-2b^2+6ab

=-2a^2+4ab-2b^2

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

=-2(a-b)^2

=-2(-2)^2

=-8