.(x+y-2)(x+y-2xy)+(xy-1)^2

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.(x+y-2)(x+y-2xy)+(xy-1)^2.(x+y-2)(x+y-2xy)+(xy-1)^2.(x+y-2)(x+y-2xy)+(xy-1)^2令x=1得f(x,y)=0;知有因式(x-1

.(x+y-2)(x+y-2xy)+(xy-1)^2
.(x+y-2)(x+y-2xy)+(xy-1)^2

.(x+y-2)(x+y-2xy)+(xy-1)^2
令x=1得f(x,y)=0;
知有因式(x-1),
代入x=1时得到 -(y-1)^2 + (y-1)^2
又x,y对称知有因式(y-1)
于是可以猜想(y-1)^2是因式,试验一下就知.
分解得(x-1)^2*(y-1)^2

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