Question

упростите выражения 1) 5(а-b)^2-(a+b)(b-a)
2) a(a-b)^2- (b-a)^3

Answer 1

$1) 5(a-b)^2-(a+b)(b-a)=5(a^2-2ab+b^2)+a^2-b^2=$$5a^2-10ab+5b^2+a^2-b^2=6a^2+4b^2-10ab$

$a(a-b)^2- (b-a)^3=a(a^2-2ab+b^2)- (b^3-3b^2a+3a^2b-a^3)=$$a^3-2a^2b+ab^2- b^3+3b^2a-3a^2b+a^3=2a^3-5a^2b+4ab^2-b^3$

Answer 2

1) 5(а-b)^2-(a+b)(b-a)=5a²-10ab+5b²-b²+a²=6a²-10ab+4b²
2) a(a-b)^2- (b-a)^3=a³-2a²b+ab²-b³+3ab²-3a²b+a³=2a³-5a²b+4ab²-b³