Question

Упростите выражение (a-b)^3+3ab(a-b)-b^3

Answer 1

(а-b)^3+3ab(a-b)-b^3=a³-3a²b+3ab²-b³++3a²b-3ab²-b³=a³-2b³

Answer 2

Вариант №1  (a-b)³+3ab(a-b)-b³=a³-3a²b+3ab²-b³+3a²b-3ab²-b=a³-2b³.
Вариант№2   (a-b)((a-b)²+3ab)-b³=((a-b)(a²-2ab+b²+3ab)-b³=
=(a-b)(a²+ab+b²)-b³=a³-b³-b³=a³-2b³.