把下列各式因式分解

题目

把下列各式因式分解
(2m+3n)(2m-n)-4n(2m-n)
(x+y)^2(x-y)+(x+y)(y-x)^2
4a(x+y)^2-2(y+x)^2

答案

(2m+3n)(2m-n)-4n(2m-n)
=(2m-n)(2m+3n-4n)
=(2m-n)(2m-n)
=(2m-n)^2
(x+y)^2(x-y)+(x+y)(y-x)^2
=(x+y)(x-y)(x+y+x-y)
=2x(x+y)(x-y)
4a(x+y)^2-2(y+x)^2
=(x+y)^2(4a-2)
=2(x+y)^2(2a-1)