还有个问题...多项式 2x^2 y^2 - 2y^2 + (xy-1)(x-1)^2 因式分解后所含有的因式是

题目

还有个问题...多项式 2x^2 y^2 - 2y^2 + (xy-1)(x-1)^2 因式分解后所含有的因式是
A.xy-1 B.x^2 - 1 C.x-1 D.(x-1)^2
究竟选哪个啊?
顺便说一说步骤...

答案

原式=2y^2(x^2-1)+(xy-1)(x-1)^2
=2y^2(x+1)(x-1)+(xy-1)(x-1)^2
=(x-1)[2y^2(x+1)+(xy-1)(x-1)]
选C