（x+y-2XY)(x+y-2)+(xy-1)^2

因式分解

2025-03-09 09:42:31

推荐回答（4个）

回答1：

（x+y-2XY)(x+y-2)+(xy-1)^2
=[（x+y)-2xy][(x+y)-2]+(xy-1)^2
=(x+y)^2-2(xy+1)(x+y)+4xy+x^2y^2-2xy+1
=(x+y)^2-2(xy+1)(x+y)+x^2y^2+2xy+1
=(x+y)^2-2(xy+1)(x+y)+(xy+1)^2
=[(x+y)-(xy+1)]^2
=(x+y-xy-1)^2
=[x(1-y)-(1-y)]^2
=(x-1)^2(1-y)^2
=(x-1)^2(y-1)^2

回答2：

(x+y-2xy)(x+y-2)+(xy-1)^2
=(x+y)^2--2(xy+1)(x+y)+(xy+1)^2
=(x+y-xy-1)^2
=(x-1)^2(y-1)^2

回答3：

[(1-x)(1-y)]^2

回答4：

暴力破解吧.