因式分解：(x-2y)乘x的3次方-(y-2x)乘y的3次方

题目

因式分解：(x-2y)乘x的3次方-(y-2x)乘y的3次方

答案

(x-2y)乘x的3次方-(y-2x)乘y的3次方
=x^4-2x^3y^-y^4+2xy^3
=(x^2+y^2)(x+y)(x-y)-2xy(x+y)(x-y)
=(x^2-2xy+y^2)(x+y)(x-y)
=(x-y)^3(x+y)