用换元法分解因式(x+y-2xy)(x+y-2)+(1-xy)^2

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用换元法分解因式(x+y-2xy)(x+y-2)+(1-xy)^2用换元法分解因式(x+y-2xy)(x+y-2)+(1-xy)^2用换元法分解因式(x+y-2xy)(x+y-2)+(1-xy)^2设

用换元法分解因式(x+y-2xy)(x+y-2)+(1-xy)^2
用换元法分解因式(x+y-2xy)(x+y-2)+(1-xy)^2

用换元法分解因式(x+y-2xy)(x+y-2)+(1-xy)^2
设x+y=a,xy=b
则(x+y-2xy)(x+y-2)+(1-xy)^2=(a-2b)(a-2)+(1-b)^2
=a^2-2ab+b^2-2a+2b+1
=(a-b)^2-2(a-b)+1
=(a-b-1)^2
=(x+y-xy-1)^2
=(x-1)^2(y-1)^2

分析的很详细,呵呵呵