Beginning Algebra, 11th Edition

Using the FOIL Method

Use the FOIL method to find the product

Step 1 F Multiply the Firstterms:

Step 2 O Find the Outerproduct:.

I Find the Innerproduct:.

Add the outer and inner products mentally:

Step 3 L Multiply the Lastterms:

First Last

Shortcut:

Inner

Outer

(^2) x Add. NOW TRY

• 6 x

(^8) x

1 x+ 821 x- 62 1 x+ 821 x- 62

x^2 - 48

1 x+ 821 x- 62 =x^2 + 2 x- 48

81 - 62 = - 48.

- 6 x+ 8 x= 2 x.

81 x 2 = 8 x

x 1 - 62 =- 6 x

x 1 x 2 =x^2.

1 x+ 821 x- 62.

NOW TRY EXAMPLE 5

EXERCISE 5
Use the FOIL method to find
the product.

1 t- 621 t+ 52

NOW TRY ANSWERS
5.t^2 - t- 30

Using the FOIL Method

Find each product.

(a)

FOI L

Multiply.

Combine like terms.

(b)

= 21 p^2 - pq- 2 q^2 FOIL

17 p+ 2 q 213 p-q 2

= 2 k^2 + 11 ky+ 15 y^2

= 2 k^2 + 6 ky+ 5 ky+ 15 y^2

= 2 k 1 k 2 + 2 k 13 y 2 + 5 y 1 k 2 + 5 y 13 y 2

12 k+ 5 y 21 k+ 3 y 2

EXAMPLE 7

NOW TRY
EXERCISE 6
Multiply.

17 y- 3212 x+ 52

NOW TRY
EXERCISE 7
Find each product.

(a)

(b) 5 x^213 x+ 121 x- 52

13 p- 5 q 214 p-q 2

6. 14 yx+ 35 y- 6 x- 15


7. (a)
   (b) 15 x^4 - 70 x^3 - 25 x^2

12 p^2 - 23 pq+ 5 q^2

Using the FOIL Method

Multiply

First

Outer

Inner

Last

FOIL

The product 19 x- 2213 y+ 12 is 27 xy+ 9 x- 6 y- 2. NOW TRY

19 x- 2213 y+ 12 - 2

19 x- 2213 y+ 12 - 6 y

19 x- 2213 y+ 12 9 x

19 x- 2213 y+ 12 27 xy

19 x- 2213 y+ 12.

EXAMPLE 6

These unlike

terms cannot

be combined.

332 CHAPTER 5 Exponents and Polynomials

NOW TRY

NOTE Alternatively, Example 7(c)can be solved as follows.

= 6 x^4 - 10 x^3 - 24 x^2 Same answer

= 12 x^3 - 6 x^2213 x+ 42

2 x^21 x- 3213 x+ 42

(c)

FOIL

= 6 x^4 - 10 x^3 - 24 x^2

= 2 x^213 x^2 - 5 x- 122

2 x^21 x- 3213 x+ 42

Distributive

property

Multiply and first.

Multiply that product and 3 x+ 4.

2 x^2 x- 3

Add the terms found

in Steps 1–3.

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