Key Concepts & Glossary | College Algebra

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Binomial Theorem

Key Concepts & Glossary

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