18.1 & 18.2: Multiplying Polynomials

Multiplying Polynomials

Each term in the first polynomial, must be multiplied by each term in the second polynomial.

Distribute!

1. a2(4 +5a3)

2. 4k2(6k – 3k4)

3. -2b2a(5b3 + 7a – 2ab3 + 4)

Method 1: Distribute

First

Outer

Inner

Last

• Multiply!!!

For Example:

Method 2: Box

Multiply (3x – 5)(5x + 2)

1. Draw a box.

2. Write a polynomial on the top and side of a box.

3. Multiply.

4. Combine like terms.

3x -5

5x

+2

Pick Your Method: (7p - 2)(3p - 4)

7p -2

3p

-4

Let’s Practice #1

1. (7x – 10)(3x + 8)

2. (2x – 3)(4x - 8)

3. (5x -10)(2x +8)

4. Trina is building a garden. She designs a rectangular garden with length (x + 4) feet and width (x + 1) feet. When x = 4, what is the area of the garden?

Let’s Practice #1

5. Orik has desiged a rectangular mural that measures 20 feet in width and 30 feet in length. Laura has also designed a rectangular mural, but it measure x feet shorter on each side. When x = 6 what is the area of Laura’s mural?

Let’s Practice #1

Multiplying Terms with Exponents

• When FOILing, add the exponents and multiply coefficients.

• Add the little numbers and multiply the big numbers!!!

Example:

(3x2 + 10x)(5x3 – 7x2)

15x5 - 21x4 + 50x4 – 70x3

15x5 + 29x4 – 70x3

Let’s Practice #2

1. (7x2 – 10x)(3x3 + 8x2)

2. (2x4 – 3x2)(4x - 8)

3. (5x3 + 2x2)(8x - 7)

Multiplying Larger Polynomials

Each term in the 1st polynomial must be multiplied by each term in the 2nd.

Example:

(7x2 + 2x + 8)(4x3 – 9x2)

x2 -5x +4

2x

-5

Method 2:

Multiply: (2x - 5)(x2 - 5x + 4)

Let’s Practice #3

1. (5x2 + 7) (2x3 – 5x2 +9)

Let’s Practice #3

2. (10x4 – 5x2 + 8) (8x3 -3x -6)

3. Mr. Silva manages a manufacturing plant. The number of units produced (in thousands) can by modeled by N(x) = 0.02x2 + 0.2x + 3, where x is the number of years. The average cost per unit (in dollars) can be modeled by C(x) = - 0.002x2 – 0.1x + 2, where x is the number of years. Write a polynomial T(x) that can be used to model Mr. Silva’s total manufacturing cost.

Let’s Practice #3

4. Brent runs a small toy store specializing in wooden toys. The number of toys made can be modeled by N(x) = – 0.7x2 – 2x + 23 and the average cost can be modeled by C(x) = -0.004x2 – 0.08x +25, where x is the number of years. Write a polynomials that can be used to model Brent’s total cost of making toys, T(x).

Let’s Practice #3