A friend of mine asked me to help with this problem. I tried induction, but I didn't know how to get this formula.
If $x$ and $y$ are real numbers such that $xy= ax+by$. Show that $ x^ny^n=\sum_{k=1}^{n}{2n-1-k \choose n-1}(a^n b^{n-k}x^k+ a^{n-k}b^n y^k), \forall n \geq 0 $
Any help is appreciated.