Question

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

Answer 1

(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