Question

分解因式:a(a-b)的三次方+2a的平方(b-a)的平方-2ab(b-a)

Answer 1

a(a-b)³+2a²(a-b)²-2ab(b-a)
= a(a-b)³+2a²(a-b)²+2ab(a-b)
=a(a-b)[(a-b)²+2a(a-b)+2b]
=a(a-b)(a²+b²-2ab+2a²-2ab+2b)
=a(a-b)(3a²+b²-4ab-2b)

Answer 2

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