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