(1+y-x^2+x^2y-2xy)(1+y-x^2+x^2y+2xy)分解因式

题目

(1+y-x^2+x^2y-2xy)(1+y-x^2+x^2y+2xy)分解因式
(1+y-x^2+x^2y-2xy)(1+y-x^2+x^2y+2xy)
最后要化成
（x-1)(xy-x-1-y)(x+1)(xy-x+1+y)
说出道理
2l
好象复杂了些..............
..............
其实应该很简单...........
1l
什么乱器八糟的..........不就是想挣分嘛........
好好答..........

答案

(1+y-x^2+x^2y-2xy)(1+y-x^2+x^2y+2xy)分解因式
=[(1-x^2)+(x^2y-2xy+y)][(1-x^2)+(x^2y+2xy+y)]
=[(1-x^2)+y(x^2-2x+1)][(1-x^2)+y(x^2+2x+1)]
=[(1+x)(1-x)+y(x-1)^2][(1+x)(1-x)+y(x+1)^2]
=(x-1)[-(x+1)+y(x-1)](x+1)[1-x+y(x+1)]
=(x-1)(xy-x-y-1)(x+1)(xy-x+y+1)