Holt McDougal Algebra 2

Multiplying Polynomials

Multiply polynomials.

Use binomial expansion to expand binomial expressions that are raised to positive integer powers.

Objectives

Holt McDougal Algebra 2

Multiplying Polynomials

Find each product.

Example 1: Multiplying a Monomial and a Polynomial

A. 4y2(y2 + 3)

B. fg(f4 + 2f3g – 3f2g2 + fg3)

Holt McDougal Algebra 2

Multiplying Polynomials

Check It Out! Example 1

Find each product.

a. 3cd2(4c2d – 6cd + 14cd2)

b. x2y(6y3 + y2 – 28y + 30)

Holt McDougal Algebra 2

Multiplying Polynomials

To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first.

Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified.

Holt McDougal Algebra 2

Multiplying Polynomials

Find the product.

Example 2A: Multiplying Polynomials

(a – 3)(2 – 5a + a2)

Holt McDougal Algebra 2

Multiplying Polynomials

(a – 3)(2 – 5a + a2)

Find the product.

Example 2A: Multiplying Polynomials

Holt McDougal Algebra 2

Multiplying Polynomials

(y2 – 7y + 5)(y2 – y – 3) Find the product.

Example 2B: Multiplying Polynomials

Holt McDougal Algebra 2

Multiplying Polynomials

Check It Out! Example 2a

Find the product.

(3b – 2c)(3b2 – bc – 2c2)

Holt McDougal Algebra 2

Multiplying Polynomials

(x2 – 4x + 1)(x2 + 5x – 2)

Find the product.Check It Out! Example 2b

Holt McDougal Algebra 2

Multiplying Polynomials

Example 3: Business Application

A standard Burly Box is p ft by 3p ft by 4p ft. A large Burly Box has 1.5 ft added to each dimension. Write a polynomial V(p) in standard form that can be used to find the volume of a large Burly Box.

Holt McDougal Algebra 2

Multiplying Polynomials

Check It Out! Example 3

Mr. Silva manages a manufacturing plant. From 1990 through 2005 the number of units produced (in thousands) can be modeled by N(x) = 0.02x2 + 0.2x + 3. The average cost per unit (in dollars) can be modeled by C(x) = –0.004x2 – 0.1x + 3. Write a polynomial T(x) that can be used to model the total costs.

Holt McDougal Algebra 2

Multiplying Polynomials

Example 4: Expanding a Power of a Binomial

Find the product.(a + 2b)3

Holt McDougal Algebra 2

Multiplying PolynomialsCheck It Out! Example 4a

Find the product.(x + 4)4

Holt McDougal Algebra 2

Multiplying PolynomialsCheck It Out! Example 4b

Find the product.(2x – 1)3

Holt McDougal Algebra 2

Multiplying PolynomialsExample 5: Using Pascal’s Triangle to Expand

Binomial ExpressionsExpand each expression.

A. (k – 5)3

Holt McDougal Algebra 2

Multiplying PolynomialsExample 5: Using Pascal’s Triangle to Expand

Binomial ExpressionsExpand each expression.

B. (6m – 8)3

Holt McDougal Algebra 2

Multiplying Polynomials

Check It Out! Example 5

Expand each expression.

a. (x + 2)3

b. (x – 4)5

Holt McDougal Algebra 2

Multiplying Polynomials

Check It Out! Example 5

c. (3x + 1)4

Expand the expression.

Holt McDougal Algebra 2

Multiplying Polynomials

4. Find the product. (y – 5)4

Lesson Quiz

2. (2a3 – a + 3)(a2 + 3a –

5) 1. 5jk(k – 2j)

3. The number of items is modeled by 0.3x2 + 0.1x + 2, and the cost per item is modeled by g(x) = –0.1x2 – 0.3x + 5. Write a polynomial c(x) that can be used to model the total cost.

Find each product.

5. Expand the expression. (3a – b)3