分解因式x^3-y^3+x^2y+xy^2

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分解因式x^3-y^3+x^2y+xy^2
分解因式x^3-y^3+x^2y+xy^2

分解因式x^3-y^3+x^2y+xy^2
x³-y³+x²y-xy²
=(x-y)(x²+xy+y²)+xy(x-y)
=(x-y)(x²+2xy+y²)
=(x-y)(x+y)²
你题目有问题
是x³-y³+x²y-xy²吧》?

x^3-y^3+x^2y+xy^2
=(x-y)(x^2+xy+y^2 )+xy(x+y)
=(x-y)[(x+y)^2-xy]+xy(x+y)
=(x-y)(x+y)^2-(x-y)xy+xy(x+y)
=(x-y)(x+y)^2-xy[(x-y)-(x+y)]
=(x-y)(x+y)^2+xy^2
怎么带个小尾巴?反正算到这里就结束了

x³-y³+x²y-xy²=(x-y)(x²+xy+y²)+xy(x-y)
=x-y)(x²+2xy+y²)
=(x-y)(x+y)²
没问题！平方数可以用“^数字”代替！

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