Hl! I have problems with demostration

Let $\displaystyle \zeta=e^{2\pi i/n}$ be a primitive nth root unity

For numbers $\displaystyle a$ and $\displaystyle b$, prove that

$\displaystyle a^n-b^n= (a-b) (a-\zeta b)(a- {\zeta}^2b) \cdot{} \cdot{} \cdot{} (a-\zeta^{n-1}b)$

and if $\displaystyle n$ is odd , that

$\displaystyle a^n+b^n= (a+b) (a+\zeta b)(a+ {\zeta}^2b) \cdot{} \cdot{} \cdot{} (a+\zeta^{n-1}b)$

Hint: Set $\displaystyle x=a/b $ if $\displaystyle b\neq{0}$

I do not know how to start or how to use the hint