因式分解:X^3-4XY^2-2XY+8Y^3

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因式分解:X^3-4XY^2-2XY+8Y^3
因式分解:X^3-4XY^2-2XY+8Y^3

因式分解:X^3-4XY^2-2XY+8Y^3
=(x^3+8y^3)-2xy(x+2y)
=(x+2y)(x^2-2xy+4y^2)-2xy(x+2y)
=(x+2y)(x^2-4xy+4y^2)
=(x+2y)(x-2y)^2

X^3-4XY^2-2X^2Y+8Y^3
=(x+2y)(x²-2xy+4y²)-2xy(2y+x)
=(x+2y)(x-2y)²