Lesson 7-7 Multiplying Polynomials

p. 447

FOIL

There are two methods that can be used to multiply polynomials

The first is called FOIL. FOIL Stands for:

First Outer Inner Last

Example

Use FOIL to solve 1. Multiply the First

Terms2. Multiply the Outer

Terms3. Multiply the Inner

Terms4. Multiply the Last

Terms5. Add the four

products and combine Like Terms

3 2x x

3 2x x 2x x x

3 2x x 2 2x x

3 2x x 3 3x x

3 2x x 3 2 6 2 2 3 6x x x

2 6x x

Use FOIL to solve

5 7x x

F

x x O

7x I

5 x L

5 7 2 7 5 35x x x

2 2 35x x 2 3 6 7y y

F

2 6y y O

2 7y I

3 6y L

3 7 212 14 18 21y y y

212 4 21y y

Problems to Try

Simplify by using the FOIL method.

1.

2.

8 4y y

6 12z z

The Distributive Property

The FOIL Method only works when you multiply two binomials

The other method used in multiplying polynomials uses the Distributive Property

The Distributive Property always works!

Example

Use the Distributive Property to Solve

1. Split the first polynomial up and write each term multiplied by the second polynomial

2. Distribute

3. Multiply

4. Combine Like Terms

3 2x x 3 2x x

32 2x xx

2 3 3 2x x x x 2 2 3 6x x x

2 6x x

Use the Distributive Property to Solve

3 2x x 2 3 2x x x 2 3 2 3x x x x 2 2 3 6x x x 2 5 6x x

24 9 2 5 3x x x FOIL would not work here!

2 24 2 5 3 9 2 5 3x x x x x 2 24 2 4 5 4 3 9 2 9 5 9 3x x x x x x x 3 2 28 20 12 18 45 27x x x x x

3 28 2 33 27x x x

Multiplying two trinomials

2 22 5 6 3 1y y y y 2 2 2 26 3 1 2 6 3 1 5 6 3 1y y y y y y y y

2 2 2 2 2 26 3 1 2 6 2 3 2 1 5 6 5 3 5 1y y y y y y y y y y y y

4 3 2 3 2 26 3 12 6 2 30 15 5y y y y y y y y

4 3 26 15 37 17 5y y y y

Problems to Try

Simplify using the Distributive Property

1.

2.

3.

5 4 2 8x x

23 4 12 1a a a

2 22 7 9 3 1b b b b

Word Problem

1. Translate the equation

2. Substitute your values

3. Simplify

11 22A h b b

12 2 3 7 2 1A x x x

12 2 5 6A x x

12 5 6 2 5 2 6A x x x x

212 5 6 10 12A x x x

212 5 4 12A x x

21 1 12 2 25 4 12A x x

252 2 6A x x

Problem to Try

1.

AlgeBlocks

2 7 10x x