1. Binomial Theorem
11.7

2. Binomial Expansion of the form (a+b)n
There are n+1 terms
Functions of n
Exponent of a in first term
Exponent of b in last term
Other terms
Exponent of a decreases by 1
Exponent of b increases by 1
Sum of exponents in each term is n
Coefficients are symmetric (Pascal’sTriangle)
At Beginning--increase
Towards End---decrease

3. Expanding Binomials
What if the term in a series is not a constant, but a binomial?

4. Pascal’s Triangle
The coefficients form a pattern, usually displayed in a triangle
Pascal’s Triangle: binomial expansion used to find the possible number of sequences for a binomial
pattern features
start and end w/ 1
coeff is the sum of the two coeff above it in the previous row
symmetric

5. Ex 1
Expand using Pascal’s Triangle

6. Ex 2
Expand using Pascal’s Triangle

7. Binomial Theorem
The coefficients can be written in terms of the previous coefficients

8. Ex 3
Expand using the binomial theorem

9. Ex 4
Expand using the binomial theorem

10. Factorials!
factorial: a special product that starts with the indicated value and has consecutive descending factors
Ex 5
Evaluate

11. Binomial Theorem, factorial form and Sigma Notation

12. Ex 6
Expand using factorial form

13. Ex 6
Expand using factorial form