x^4y-x^3y^2-x^2y^3+xy^4因式分解

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

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

第一项和第四项合并再用立方和公式，二三项只提取公因数，之后你就会了

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

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