因式分解：(x+y)的2次方(x减y)+(x减y)(y减x)的两次方

题目

因式分解：(x+y)的2次方(x减y)+(x减y)(y减x)的两次方
输错了，后面是（x+y)(y-x)^2

答案

(x+y)²(x-y)+(x+y)(y-x)²
=(x+y)(x+y)(x-y)+(x+y)(x-y)(x-y)
=(x+y)[(x+y)(x-y)+(x-y)(x-y)]
=(x+y)[(x-y)(x+y+x-y)]
=(x+y)(x-y)2x