Binomial Theorem: An Inductive Proof

Binomial Theorem: An Inductive Proof

I'm asked to use the fact that
$\begin{pmatrix}n\\r\end{pmatrix}+\begin{pmatrix}n\\r-1\end{pmatrix}=\begin{pmatrix}n+1\\r\end{pmatrix}$
to show, by induction, that
$$(a+b)^n=\begin{pmatrix}n\\0\end{pmatrix}a^n+\begin{pmatrix}n\\1\end{pmatrix}a^{n-1}b+\cdots+\begin{pmatrix}n\\r\end{pmatrix}a^{n-r}b^r+\begin{pmatrix}n\\n\end{pmatrix}b^n,$$
but I'm not sure where to start. I suspect that for the inductive step I
multiply both sides by $(a+b)$, but from there I'm not sure where to go.