（x+y-2xy）（x+y-2）+（xy-1）²
=（x+y）²-2xy（x+y）-2（x+y）+4xy+x²y²-2xy+1
=（x+y）²-2（x+y）（xy+1）+（xy+1）²
=（x+y-xy-1）²
=（x-1）²•（y-1）²．
故答案为（x-1）²•（y-1）²．