因式分解:(x的平方-y的平方)(x+y)-(x-y)的三次方

问题描述:

因式分解:(x的平方-y的平方)(x+y)-(x-y)的三次方

(x^2-y^2)(x+y)-(x-y)^3
=(x+y)(x-y)(x+y)-(x-y)^3
=(x-y)[(x+y)^2-(x-y)^2]
=(x-y)[(x+y)+(x-y)][(x+y)-(x-y)]
=(x-y)*2x*2y
=4xy(x-y)