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Study Guides > College Algebra

Key Concepts & Glossary

Key Equations

Binomial Theorem (x+y)n=k0n(nk)xnkyk{\left(x+y\right)}^{n}=\sum _{k - 0}^{n}\left(\begin{array}{c}n\\ k\end{array}\right){x}^{n-k}{y}^{k}
(r+1)th\left(r+1\right)th term of a binomial expansion (nr)xnryr\left(\begin{array}{c}n\\ r\end{array}\right){x}^{n-r}{y}^{r}

Key Concepts

  • (nr)\left(\begin{array}{c}n\\ r\end{array}\right) is called a binomial coefficient and is equal to C(n,r)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(n,r)C\left(n,r\right), denoted (nr)\left(\begin{array}{c}n\\ r\end{array}\right)
binomial expansion
the result of expanding (x+y)n{\left(x+y\right)}^{n} by multiplying
Binomial Theorem
a formula that can be used to expand any binomial
 

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  • Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution.