Using the Binomial Theorem to Find a Single Term
Expanding a binomial with a high exponent such as can be a lengthy process. Sometimes we are interested only in a certain term of a binomial expansion. We do not need to fully expand a binomial to find a single specific term. Note the pattern of coefficients in the expansion of .
The second term is . The third term is . We can generalize this result.
A General Note: The (r+1)th Term of a Binomial Expansion
The term of the binomial expansion of is:How To: Given a binomial, write a specific term without fully expanding.
- Determine the value of according to the exponent.
- Determine .
- Determine .
- Replace in the formula for the term of the binomial expansion.