求解一道数学题；（xy-1)^2+(x+y-2)(x+y-2xy) 分解因式

分类: 作业答案 • 2023-01-14 10:02:23

问题描述：

答

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