x^3-4xy^2-2x^2y+8y 因式分解

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x^3-4xy^2-2x^2y+8y因式分解x^3-4xy^2-2x^2y+8y因式分解x^3-4xy^2-2x^2y+8y因式分解题目有错?x^3-4xy^2-2x^2y+8y?x^3-4xy^2-

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

x^3-4xy^2-2x^2y+8y 因式分解
题目有错?
x^3-4xy^2-2x^2y+8y?x^3-4xy^2-2x^2y+8y^3?
(x+2y)^3=x^3+6x^2y+12xy^2+8y^3,
x^3-4xy^2-2x^2y+8y^3=(x+2y)^3-8x^2y-16xy^2=(x+2y)^3-8xy(x+2y)=(x+2y)[(x+2y)^2-8xy]
=(x+2y)(x-2y)^2

=x^3-4xy^2+8y^3-4xy^2
=x^2(x-2y)+4y^2(2y-x)
=x^2(x-2y)-4y^2(2y-x)
=(x^2-4y^2)(2y-x)
=(x+2y)(x-2y)(2y-x)