1. 2-6 Binomial Theorem 1 2 3 Factorials
Pascal’s Triangle & Binomial Theorem 3
Practice Problems

2. Factorials
Written as “n!”
Used in the Binomial Theorem and Statistics

3. Simplifying Factorial Expressions
Evaluate

4. Pascal’s Triangle
Expanding the Powers of b+g

5. Coefficients of Pascal’s Triangle

6. Coefficients of Pascal’s Triangle
Observations for Each Row in the form of (a+b)n
There are n+1 terms
n is the exponent of a in the first term and the exponent of b in the last term
In each term, the exponent of a decreases by one and the exponent of b increases by one
The sum of the exponents in each term is n
The coefficients are symmetric. They increase at the beginning and decrease at the end

7. Constructing Pascal’s Triangle
Each number in the triangle is the sum of the two directly above it.

8. Sums of the Rows of Pascal’s Triangle

9. “Magic 11’s” of Pascal’s Triangle

10. Binomial Theorem If n is a non-negative integer, then
So to expand (x+y)4…
Does look familiar?

11. Binomial Theorem Example
Expand (2x+y)5
Remember Pascal’s Triangle for (a+b)5
Follow the pattern of the exponents
Simplify

12. Practice Problems