Question

分解因式：(x+y-2xy)(x+y-2)+(xy-1)^2

Answer 1

=(x+y)²-2(x+y)-2xy(x+y)+4xy+x²y²-2xy+1
=(x+y)²-2(x+y)(xy+1)+x²y²+2xy+1
=(x+y)²-2(x+y)(xy+1)+(xy+1)²
=(x+y-xy-1)²
=(x-1)²(1-y)²

其中：x+y-xy-1
=x-xy+y-1
=x(1-y)-(1-y)
=(x-1)(1-y)
上面可直接写出

Answer 2

5×[xy+(1+根号下141）/10]×[xy+(1-根号下141）]
解法：设xy＝z
则原式＝5z2＋z－7
设5z2＋z－7＝0
求出该方程的两个解，带入原因式可得上述结果

Answer 3

(x+y-2xy)(x+y-2)+(xy-1)^2
=[(x+y)-2xy]* [(x+y)-2] +(xy-1)^2
=（x+y）^2 - 2xy * (x+y) -2(x+y)+4xy + （xy）^2+ 1- 2xy
=x^2+ y^2+(xy)^2-2x^2y -2xy^2+4xy-2x-2y+1

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Answer 4

（x+y-2XY)(x+y-2)+(xy-1)^2
=[（x+y)-2xy][(x+y)-2]+(xy-1)^2
=(x+y)^2-2(xy+1)(x+y)+4xy+x^2y^2-2xy+1
=(x+y)^2-2(xy+1)(x+y)+x^2y^2+2xy+1
=(x+y)^2-2(xy+1)(x+y)+(xy+1)^2
=[(x+y)-(xy+1)]^2
=(x+y-xy-1)^2
=[x(1-y)-(1-y)]^2
=(x-1)^2(1-y)^2
=(x-1)^2(y-1)^2