分解因式:(x+y-2xy)(x+y-2)+(xy+1)²=?题打错了是xy-1

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分解因式:(x+y-2xy)(x+y-2)+(xy+1)²=?题打错了是xy-1分解因式:(x+y-2xy)(x+y-2)+(xy+1)²=?题打错了是xy-1分解因式:(x+y-

分解因式:(x+y-2xy)(x+y-2)+(xy+1)²=?题打错了是xy-1
分解因式:(x+y-2xy)(x+y-2)+(xy+1)²=?
题打错了
是xy-1

分解因式:(x+y-2xy)(x+y-2)+(xy+1)²=?题打错了是xy-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+x²y²-2xy+1
=(x+y)²-2(xy+1)(x+y)+x²y²+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