(x+y-2xy)(x+y-2)+(xy-1)²因式分解

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(x+y-2xy)(x+y-2)+(xy-1)²因式分解
(x+y-2xy)(x+y-2)+(xy-1)²因式分解

(x+y-2xy)(x+y-2)+(xy-1)²因式分解
(x+y-2xy)(x+y-2)+(xy-1)²
=(x+y)²-(2xy+2)(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