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

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Presentation transcript:

Copyright © 2011 Pearson, Inc. 9.2 The Binomial Theorem

Copyright © 2011 Pearson, Inc. Slide 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.

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

Copyright © 2011 Pearson, Inc. Slide Binomial Coefficient

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

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

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

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

Copyright © 2011 Pearson, Inc. Slide The Binomial Theorem

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

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

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

Copyright © 2011 Pearson, Inc. Slide Basic Factorial Identities

Copyright © 2011 Pearson, Inc. Slide Quick Review

Copyright © 2011 Pearson, Inc. Slide Quick Review Solutions

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