Question

因式分解x^6 (x-y)^2n+1 + y^6 (y-x)^2n+1

Answer 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)