Question

因式分解 (x+y-2xy)(x+y-2)(xy-1)^2 完整过程!!!

Answer 1

（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

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Answer 2

(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
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Answer 3

解；（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

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