因式分解（x+y-2xy)(x+y-2)+(xy-1)^2
问题描述：
因式分解（x+y-2xy)(x+y-2)+(xy-1)^2
设x+y=a,xy=b,
答
(a-2b)(a-2)+(b-1)^2
=a^2-2ab-2a+4b+b^2-2b+1
=a^2-2ab-2a+b^2+2b+1
=a^2-2ab+b^2-2a+2b+1
=(a-b)^2-2(a-b)+1
=(a-b-1)^2