Question

暑假作业因式分解(x+y-2xy)(x+y)+(xy-1)2

Answer 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