分解因式：(x+y-2xy)(x+y-2)+(xy-1)²?

分类: 作业答案 • 2022-05-30 11:24:35

问题描述：

分解因式：(x+y-2xy)(x+y-2)+(xy-1)²?
(xy - x - y + 1)^2=(x+1)^2*(y+1)^2?

答

答案是
(x + y - 2xy)(x + y - 2) + (xy - 1)^2
= (xy - x - y + 1)^2
凑一凑就出来了.
(xy - x - y + 1)^2=(x-1)^2*(y-1)^2
因为：xy - x - y + 1=(x-1)*(y-1)