Binomial ExpansionHonors Advanced AlgebraPresentation 2-3
Warm-up Multiply the following polynomials.1. (x + 3)(3x2 + 2)
2. (m + 3)(m + 4)(m + 1)
3. (k + 3)(k + 1)(k2 – 5)
4. 5a(a – 1)(a + 2)2
Factorials Used in counting problems. Calculation
formula:
Factorials
Example 1: 5!
5 ∙ 4 ∙ 3 ∙ 2 ∙ 1
120
Factorials
Example 2: 8!
8 ∙ 7 ∙ 6 ∙ 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1
40,320
Combinations Used in counting problems when order
does not matter. Calculation formula:
nCr =
Combinations
Example 1: 5C2
Combinations
Example 2: 12C4
Combinations
Example 3: 12C8
You Try!1. 6!2. 7C33. 9C84. 18C15
720
35
9
816
Simplifying Combinations
nCr = nCn-r
Example: 20C16 = 20C4
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.
Pascal’s Triangle Tool used to
help expandbinomials
Each row createdby adding numbersabove
First row is the 0th
row
Pascal’s Triangle
4C1
8C5
(a + b)0 = 1
(a + b)1 = 1a+1b(a + b)2 = 1a2+2ab+1b2(a + b)3 = 1a3+3a2b+3ab2+1b3
(a + b)4
(a + b)5
(a + b)6
(a + b)7
(a + b)8
(a + b)9
(a + b)10
(a + b)11
Expanding a Binomial Expand (a + b)5
Expanding a Binomial Expand (x + 2)4
You Try!1. Expand (x - 3)3
2. Expand (2x + 1)4
3. Expand (3x - 1)5
4. Expand (3x + 2)6
Homework Pg. 94 - 95, #2 - 5, 9 -12, 19, 20