因式分解x^6 (x-y)^2n+1 + y^6 (y-x)^2n+1

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因式分解x^6 (x-y)^2n+1 + y^6 (y-x)^2n+1
因式分解x^6 (x-y)^2n+1 + y^6 (y-x)^2n+1

因式分解x^6 (x-y)^2n+1 + y^6 (y-x)^2n+1
先说公式
x^(2n+1)=-[(-x)^(2n+1)]
立方和公式：x³+y³=(x+y)(x²-xy+y²)
立方差公式：x³-y³-(x-y)(x²+xy+y²)
x^6 (x-y)^2n+1 + y^6 (y-x)^2n+1
=x^6 (x-y)^2n+1 - y^6 (x-y)^2n+1
=[(x-y)^(2n+1)](x^6-y^6)
=[(x-y)^(2n+1)][(x³)²-(y³)²]
=[(x-y)^(2n+1)](x³-y³)(x³+y³)
=[(x-y)^(2n+1)](x+y)(x²-xy+y²)(x-y)(x²+xy+y²)

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