x2+Xy-2Y2=0是如何变成(x-y)(x+2Y)

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x2+Xy-2Y2=0是如何变成(x-y)(x+2Y)

x2+Xy-2Y2=0是如何变成(x-y)(x+2Y)
x2+Xy-2Y2=0是如何变成(x-y)(x+2Y)

x2+Xy-2Y2=0是如何变成(x-y)(x+2Y)
十字交乘法:
x +2y
x -y
=(x-y)(x+2y)

把y看成常数,求解x,得x=y或x=-2y,所以x2+xy-2y2=(x-y)(x+2y)

因式分解
把x^2分解为x与x
把-2y^2分解为+2y与-y
故x2+Xy-2Y2
=(x+2y)(x-y)