An extension to the binomial theorem. It gives the expansion of a multinomial $(x_0,\dots,x_{m-1})^n$.
For terms $(x_j)_{j=0}^{m-1}$ and natural number $n$, we have $$ \left(\sum_{j=0}^{m-1} x_j \right)^n = \sum_{\sum_{j=0}^{m-1} k_j = n} \binom{n}{k_0,k_1,\dots,k_{m-1}} \prod_{j=0}^{m-1} x_j^{k_j} $$ where $\binom{\cdot}{\cdot}$ is the multinomial coefficient $$ \binom{n}{k_0,k_1,\dots,k_{m-1}} = \frac{n!}{k_0!k_1!\cdots k_{m-1}!} $$
