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