x^3-4xy^2-2x^2y+8y 因式分解

问题描述:

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