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题目
因式分解:(x+y-2xy)(x+y-2)+(1-xy)2=______.

提问时间:2021-03-23

答案
(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
故答案为:(x+y-1-xy)2
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