Key Concepts & Glossary
Key Equations
| Binomial Theorem | [latex]{\left(x+y\right)}^{n}=\sum _{k - 0}^{n}\left(\begin{array}{c}n\\ k\end{array}\right){x}^{n-k}{y}^{k}[/latex] |
| [latex]\left(r+1\right)th[/latex] term of a binomial expansion | [latex]\left(\begin{array}{c}n\\ r\end{array}\right){x}^{n-r}{y}^{r}[/latex] |
Key Concepts
- [latex]\left(\begin{array}{c}n\\ r\end{array}\right)[/latex] is called a binomial coefficient and is equal to [latex]C\left(n,r\right)[/latex].
- 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 [latex]C\left(n,r\right)[/latex], denoted [latex]\left(\begin{array}{c}n\\ r\end{array}\right)[/latex]
- binomial expansion
- the result of expanding [latex]{\left(x+y\right)}^{n}[/latex] by multiplying
- Binomial Theorem
- a formula that can be used to expand any binomial
Licenses & Attributions
CC licensed content, Specific attribution
- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.
