1. The Binomial Theorem

2. (x + y) 0 Find the patterns: 1 (x + y) 1 x + y (x + y) 2 (x + y) 3 x 3 + 3x 2 y + 3xy 2 + y 3 (x + y) 4 (x + y) 0 (x + y) 1 (x + y) 2 (x + y) 3 (x + y) 4 x 1 + y 1 x 2 + 2xy + y 2 x 3 + 3x 2 y 1 + 3x 1 y 2 + y 3 x 4 + 4x 3 y + 6x 2 y 2 +4xy 3 + y 4 x 3 y 0 + 3x 2 y 1 + 3x 1 y 2 + x 0 y 3 (x + y) 6 x 6 + 6x 5 y + 15x 4 y 2 +20x 3 y 3 + 15x 2 y 4 + 6x 1 y 5 + y 6 Notice how the exponents of each term sum to “ n “. What about the coefficients of each term? Is there a pattern there?

3. 1 1 1 1 1 2 1 1 3 3 1 1446 1 1 5 5 10 0 1 2 3 4 5

4. Finding the Coefficient of a Binomial using a Formula.

5. x x x 3

7. x x x 2

8. 1 What about the coefficients of each term? Is there a pattern there? 1 1 1 1 2 1 1 3 3 1 1446 1 1 5 5 10 0 1 2 3 4 5