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 • 2021-12-20 04:43:19

问题描述：

答

(xy-1)^2+(x+y-2)(x+y-2xy)
=(xy)^2-2xy-1+x^2+y^2+2xy-2x-2y-4xy-2yx^2-2xy^2
=(xy)^2-10xy-1+(xy)^2-(2xy+2)(x+y)
=(4xy+2)(x+y)-10xy

答

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

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