因式分解x^3-4xy^2-2x^2y+8y^3

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因式分解x^3-4xy^2-2x^2y+8y^3
因式分解x^3-4xy^2-2x^2y+8y^3

因式分解x^3-4xy^2-2x^2y+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(x^2-4y^2)-2y(x^2-4y^2)
=x(x+2y)(x-2y)-2y(x+2y)(x-2y)
=(x-2y)^2(x+2y)

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