一题初一的因式分解(x-2y)x^3-(y-2x)y^3

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一题初一的因式分解(x-2y)x^3-(y-2x)y^3
一题初一的因式分解
(x-2y)x^3-(y-2x)y^3

一题初一的因式分解(x-2y)x^3-(y-2x)y^3
(x-2y)x^3-(y-2x)y^3
=(x^4-2x^3y-y^4+2xy^3)
=[x^2+y^2][x^2-y^2]-2xy[x^2-y^2]
=[x^2-y^2][x^2+y^2-2xy]
=[x+y][x-y][x-y]^2
=[x+y][x-y]^3

原式=(X+Y)³(X-Y)

(x-2y)x^3-(y-2x)y^3
=x^4-2yx^3-y^4+2xy^3
=(x^2+y^2)(x-y)(x+y)-2xy(x-y)(x+y)
=(x-y)(x+y)(x-y)^2
=(x-y)^3(x+y)