> [!NOTE] Lemma > For $n \in \mathbb{N}$, $(a+b)^{n} = \sum_{k=0}^{n} {n \choose k} a^{k}b^{n-k}$where $\binom{n}{k}$ is a [[Binomial Coefficient|binomial coefficient]]. ###### Proof Use induction and [[Pascal's Identity for Binomial Coefficients]]. $\blacksquare$ ###### Proof Follows from [[Multinomial Theorem]]. $\blacksquare$