1. Binomial Theorem
and Pascal’s Triangle

2. Binomial Theorem

3. Pascals Triangle 1 2 3 4 6 5 10 15 20 7 21 35

5. Binomial Theorem Notice each expression has n + 1 terms
The degree of each term is equal to n
The exponent of each a decreases by 1 and the exponent of each b increases by 1 for each succeeding term in the series
The coefficients come from Pascal’s Triangle
In subtraction alternate signs starting with positive then negative

6. Expand using the Binomial Theorem and Pascal’s Triangle

7. Binomial Theorem
Write the general rule for the binomial using Pascal’s Triangle
Substitute into the general rule
Simplify your expression

8. Expand using the Binomial Theorem and Pascal’s Triangle

9. Use the previous term method to determine each of the following

10. Factorial
If n > 0 is an integer, the factorial symbol n! is defined as follows:
0! = 1 and 1! = 1
n! = n(n – 1) •… • 3 • 2 • 1 if n > 2
4! = 4 • 3 • 2 • 1 = 24
6! = 6 • 5 • 4 • 3 • 2 • 1 = 720

11. Factorial

12. Evaluate the following expressions

13. We can use the Binomial Theorem to find a particular term in an expression without writing the entire expansion.