## Key Equations

 Binomial Theorem ${\left(x+y\right)}^{n}=\sum _{k - 0}^{n}\left(\begin{array}{c}n\\ k\end{array}\right){x}^{n-k}{y}^{k}$ $\left(r+1\right)th$ term of a binomial expansion $\left(\begin{array}{c}n\\ r\end{array}\right){x}^{n-r}{y}^{r}$

## Key Concepts

• $\left(\begin{array}{c}n\\ r\end{array}\right)$ is called a binomial coefficient and is equal to $C\left(n,r\right)$.
• The Binomial Theorem allows us to expand binomials without multiplying.
• We can find a given term of a binomial expansion without fully expanding the binomial.

## Glossary

binomial coefficient
the number of ways to choose r objects from n objects where order does not matter; equivalent to $C\left(n,r\right)$, denoted $\left(\begin{array}{c}n\\ r\end{array}\right)$
binomial expansion
the result of expanding ${\left(x+y\right)}^{n}$ by multiplying
Binomial Theorem
a formula that can be used to expand any binomial