2017 Precalculus Section 11­5 Binomial Theorem.notebook
April 03, 2017
Monday, April 3
Binomial Theorem
Precalculus
Expand each binomial.
1.
2.
The Binomial Theorem is a formula for the
expansion of
for any positive integer n.
3.
Apr 5­7:38 AM
• Before we can understand the binomial
theorem, we need to define the symbol
read “the combination of n things taken
r at a time”
Apr 5­7:48 AM
Apr 5­7:46 AM
Evaluating
Apr 5­7:49 AM
1
2017 Precalculus Section 11­5 Binomial Theorem.notebook
Four Useful Formulas
Apr 5­7:50 AM
April 03, 2017
Binomial Theorem
• Let x and a be real numbers. For
any positive integer n, we have
Apr 5­7:51 AM
Example
Use the binomial theorem to expand.
Apr 5­7:53 AM
Apr 3­9:15 AM
2
2017 Precalculus Section 11­5 Binomial Theorem.notebook
To find a particular term in the expansion of
April 03, 2017
Example
Find the 6th term in the expansion of
where r is one less than the term
number.
Apr 5­7:54 AM
Another way to expand
a binomial is by using
1
Pascal's Triangle.
1
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
Apr 5­8:01 AM
Apr 5­7:56 AM
Example
Use Pascals Triangle to expand.
1
1 2 1
3
3
1
4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
7 1
1 7 21 35 35 21
1
1
4
6
Apr 5­8:28 AM
3
2017 Precalculus Section 11­5 Binomial Theorem.notebook
April 03, 2017
Assignment:
Worksheet 11-5
Apr 5­7:57 AM
4