1. Copyright © 2011 Pearson, Inc. 9.2 The Binomial Theorem

2. Copyright © 2011 Pearson, Inc. Slide 9.2 - 2 What you’ll learn about Powers of Binomials Pascal’s Triangle The Binomial Theorem Factorial Identities … and why The Binomial Theorem is a marvelous study in combinatorial patterns.

3. Copyright © 2011 Pearson, Inc. Slide 9.2 - 3 Powers of Binomials If you expand (a + b) n for n = 0, 1, 2, 3, 4, and 5, here is what you get:

4. Copyright © 2011 Pearson, Inc. Slide 9.2 - 4 Binomial Coefficient

5. Copyright © 2011 Pearson, Inc. Slide 9.2 - 5 Example Using n C r to Expand a Binomial

6. Copyright © 2011 Pearson, Inc. Slide 9.2 - 6 Example Using n C r to Expand a Binomial

7. Copyright © 2011 Pearson, Inc. Slide 9.2 - 7 Pascal’s Triangle

8. Copyright © 2011 Pearson, Inc. Slide 9.2 - 8 Recursion Formula for Pascal’s Triangle

9. Copyright © 2011 Pearson, Inc. Slide 9.2 - 9 The Binomial Theorem

10. Copyright © 2011 Pearson, Inc. Slide 9.2 - 10 Example Expanding a Binomial

11. Copyright © 2011 Pearson, Inc. Slide 9.2 - 11 Example Expanding a Binomial

12. Copyright © 2011 Pearson, Inc. Slide 9.2 - 12 Example Expanding a Binomial

13. Copyright © 2011 Pearson, Inc. Slide 9.2 - 13 Basic Factorial Identities

14. Copyright © 2011 Pearson, Inc. Slide 9.2 - 14 Quick Review

15. Copyright © 2011 Pearson, Inc. Slide 9.2 - 15 Quick Review Solutions