1. Binomial Expansion Honors Advanced Algebra Presentation 2-3

2. Warm-up  Multiply the following polynomials. 1. (x + 3)(3x 2 + 2) 2. (m + 3)(m + 4)(m + 1) 3. (k + 3)(k + 1)(k 2 – 5) 4. 5a(a – 1)(a + 2) 2

3. Factorials

4. Example 1: 5! 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 120

5. Factorials Example 2: 8! 8 ∙ 7 ∙ 6 ∙ 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 40,320

6. Combinations

7. Example 1: 5 C 2

8. Combinations Example 2: 12 C 4

9. Combinations Example 3: 12 C 8

10. You Try! 1. 6! 2. 7 C 3 3. 9 C 8 4. 18 C 15 720 35 9 816

11. Simplifying Combinations n C r = n C n-r Example: 20 C 16 = 20 C 4

12. Vocabulary  Binomial Expansion – Finding the polynomial of a binomial raised to a power greater than 1.  Pascal’s Triangle – Mathematical tool used to calculate the coefficients of a binomial expansion.

13. Pascal’s Triangle  Tool used to help expand binomials  Each row created by adding numbers above  First row is the 0 th row

14. Pascal’s Triangle 4C14C1 8C58C5 (a + b) 0 = 1 (a + b) 1 = 1a+1b (a + b) 2 = 1a 2 +2ab+1b 2 (a + b) 3 = 1a 3 +3a 2 b+3ab 2 +1b 3 (a + b) 4 (a + b) 5 (a + b) 6 (a + b) 7 (a + b) 8 (a + b) 9 (a + b) 10 (a + b) 11

15. Expanding a Binomial  Expand (a + b) 5

16. Expanding a Binomial  Expand (x + 2) 4

17. You Try! 1. Expand (x - 3) 3 2. Expand (2x + 1) 4 3. Expand (3x - 1) 5 4. Expand (3x + 2) 6

18. Homework  Pg. 94 - 95, #2 - 5, 9 -12, 19, 20