一道初二年级因式分解题````请各位帮个忙~~谢了 ~

解:
原式=(xy-1)^2+[(x+y)-2xy](x+y-2)
=[(xy-1)^2-4xy]+(x+y)^2-2xy(x+y)-2(x+y)
=(xy+1)^2-2(x+y)(xy+1)+(x+y)^2
=(xy+1-x-y)^2
=(x-1)^2*(y-1)^2

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

=x^2*y^2+4xy+1-2x+x^2+y^2+2x^2*y+2xy^2

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