因式分解:(x-y)^2(m-n)+(x+y)^2(n-m)

问题描述:

因式分解:(x-y)^2(m-n)+(x+y)^2(n-m)

答:
(x-y)^2(m-n)+(x+y)^2(n-m)
=(m-n)*[(x-y)^2-(x+y)^2]
=(m-n)*(x-y+x+y)*(x-y-x-y)
=(m-n)*(2x)*(-2y)
=-4(m-n)xy