把x( 3)-4xy( 2)-2x( 2)y+8y( 3)因式分解,写出具体过程.

来源：学生作业帮助网编辑：作业帮时间：2024/05/26 08:04:25

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

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+4y^2)
注:x^3+8y^3用立方和公式分解

原式=x(x^2-4y^2)-2y(x^2-4y^2)
=(x-2y)(x^2-4y^2)
=(x-2y)(x+2y)(x-2y)
=(x+2y)(x-2y)^2

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