Intermediate Algebra (11th edition)

To get 9x, the outerterms are multiplied.

Outer terms

The term comes from the innerterms.

Inner terms

Finally, comes from the lastterms.

Last terms

The product is found by adding these four results.

FOIL

Combine like terms.

To keep track of the order of multiplying terms, we use the initials FOIL (First,

Outer, Inner, Last). This procedure can be written in compact form as follows.

First Last

Inner

Outer

(^) x Add.
9 x

• 8 x

13 x- 4212 x+ 32 13 x- 4212 x+ 32

6 x^2 - 12

= 6 x^2 + x- 12

= 6 x^2 + 9 x+ 1 - 8 x 2 + 1 - 122

13 x- 4212 x+ 32

13 x- 4212 x+ 32 - 4132 = - 12

- 12

13 x- 4212 x+ 32 - 412 x 2 = - 8 x

- 8 x

13 x- 4212 x+ 32 3 x 132 = 9 x

SECTION 5.4 Multiplying Polynomials 295

Try to do as many of these

steps as possible mentally.

Using the FOIL Method

Use the FOIL method to find each product.

(a)

First terms

Outer terms

Inner terms

Last terms

F OIL

= 12 m^2 - 11 m- 5 Combine like terms.

= 12 m^2 + 4 m- 15 m- 5

14 m- 5213 m+ 12

14 m- 5213 m+ 12 - 5112 = - 5

14 m- 5213 m+ 12 - 513 m 2 = - 15 m

14 m- 5213 m+ 12 4 m 112 = 4 m

14 m- 5213 m+ 12 4 m 13 m 2 = 12 m^2

14 m- 5213 m+ 12

EXAMPLE 4

CAUTION The FOIL method applies only to multiplying two binomials.

First, is the product of the two firstterms.

13 x- 4212 x+ 32 3 x 12 x 2 = 6 x^2 First terms

6 x^2