(x+y-2xy)(x+y-2)+(1-xy)²
=(x+y)²-2(1+xy)(x+y)+4xy+1-2xy+x²y²
=(x+y)²-2(1+xy)(x+y)+(1+xy)²
=(x+y)²-(1+xy)(x+y)-(1+xy)(x+y)+(1+xy)²
=(x+y)(x+y-1-xy)-(1+xy)(x+y-1-xy)
=(x+y-1-xy)(x+y-1-xy)
=(x+y-1-xy)²