(xy-1)²+(x+y-2xy)(x+y-2)分解因式用换元法
问题描述：
(xy-1)²+(x+y-2xy)(x+y-2)分解因式用换元法
答
令a=x+y-2xyb=x+y-2b-a=2xy-2=2(xy-1)所以原式=[(b-a)/2]²+ab=(b²-2ab+b²+4ab)/4=(a²+2ab+b²)/4=(a+b)²/4=(2x+2y-2xy-2)²/4=(xy-x-y+1)²=(x-1)²(y-1)²