作业帮一道高一因式分解练习题(x+y-2xy)(x+y-2)+(xy-1)^2
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一道高一因式分解练习题(x+y-2xy)(x+y-2)+(xy-1)^2
一道高一因式分解练习题
(x+y-2xy)(x+y-2)+(xy-1)^2
一道高一因式分解练习题(x+y-2xy)(x+y-2)+(xy-1)^2
(x+y-2xy)(x+y-2)+(xy-1)^2
=[(x+y)-2xy][(x+y)-2]+(xy-1)²
=(x+y)²-2(x+y)-2xy(x+y)+4xy+(xy-1)²
=(x+y)²-[2(x+y)+2xy(x+y)]+[(xy-1)²+4xy]
=(x+y)²-2[(x+y)+xy(x+y)]+(x²y²-2xy+4xy+1)
=(x+y)²-2(x+y)(xy+1)+(xy+1)²
=(xy+1-x-y)²
=[(xy-y)-(x-1)]²
=[y(x-1)-(x-1)]²
=(y-1)²(x-1)²
全部拆开
=X^2+Y^2-2XY-2(X+Y)-2XY(X+Y)+X^2Y^2+1+2XY
=(X+Y)^2-2(X+Y)(XY+1)+(XY+1)^2
=(X+Y-XY-1)^2
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