1. Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Chapter 8
Sequences,
Induction, and
Probability
8.5 The Binomial Theorem
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1

2. Objectives:
Evaluate a binomial coefficient.
Expand a binomial raised to a power.
Find a particular term in a binomial expansion.

3. Definition of a Binomial Coefficient

4. Example: Evaluating Binomial Coefficients
Evaluate each of the following:

5. Example: Evaluating Binomial Coefficients
Evaluate:

6. A Formula for Expanding Binomials: The Binomial Theorem

7. Example: Using the Binomial Theorem
Expand:

8. Example: Using the Binomial Theorem (continued)
Expand:

9. Finding a Particular Term in a Binomial Expansion
The (r + 1)st term of the expansion of (a + b)n is

10. Example: Finding a Single Term of a Binomial Expansion
Find the fifth term in the expansion of
The fifth term in the expansion of (2x + y)9 is