一道有趣的数学题,奖分,因式分解(xy-1)^+(x+y-2)(x+y-2xy)^为二次方

Question

一道有趣的数学题,奖分,
因式分解(xy-1)^+(x+y-2)(x+y-2xy)
^为二次方

Answer 1

令x+y=a,xy=b
原式化为：
（b-1）^2+(a-2)(a-2b)
=b^2-2b+1+a^2-2a-2ab+4b
=b^2+2b+1+a^2-2a-2ab
=(a^2-2ab+b^2)+2(b-a)+1
=(b-a)^2+2(b-a)+1
=(b-a+1)^2
=(xy-x-y+1)^2
=(x-1)^2*(y-1)^2