Page 743 - Basic College Mathematics with Early Integers

A PPEND I X B . 3 I MULTIPLYING POLYNOMIALS 719

FOIL stands for the products of the First terms, Outer terms, Inner terms, then
Last terms. For example,

L
F
Î Î Î Î F O I L 2
#
#
#
#
1x + 221x + 32 = x x + x 3 + 2 x + 2 3 = x + 3x + 2x + 6
Î
Î
Î
Î
2
= x + 5x + 6 The product is
I
c
O
the same no matter what order
or method you choose to use.
Examples Use the FOIL order to multiply. PRACTICE 6–7
L Use the FOIL order to multiply.
F F O I L
Î Î Î Î 6. (10x - 7)(x + 3)
#
#
6. 13x - 6212x + 12 = 3x 2x + 3x 1 + 1-6212x2 + 1-62112 2
2
= 6x + 3x - 12x - 6 Multiply. 7. (3x + 2)
Î
Î
Î
Î
2
I
= 6x - 9x - 6 Combine like terms.
O
2
7. 13x - 52 = 13x - 5213x - 52
F O I L
#
= 3x 3x + 3x1-52 + 1-5213x2 + 1-521-52
2
= 9x - 15x - 15x + 25 Multiply.
2
= 9x - 30x + 25 Combine like terms.
Work Practice 6–7
Remember that the FOIL order can only be used to multiply two binomials.

Objective Multiplying Polynomials

Recall from Appendix B.1 that a polynomial that consists of exactly three terms is
called a trinomial. Next, we multiply a binomial by a trinomial.

Example 8 Multiply: 13a + 221a - 6a + 32 PRACTICE 8
2
Multiply:
Solution: Use the distributive property to multiply 3a by the trinomial (2x + 5)(x + 4x - 1)
2
2
1a - 6a + 32 and then 2 by the trinomial.
Apply the
2
2
2
(3a+2)(a -6a+3)=3a(a -6a+3)+2(a -6a+3) distributive
#
#
2
=3a a +3a(–6a)+3a 3+ property.
#
#
2
2 a +2(–6a)+2 3 Apply the
distributive property.
2
2
3
=3a -18a +9a+2a -12a+6 Multiply.
3
2
=3a -16a -3a+6 Combine like terms. Answers
2
6. 10x + 23x - 21
Work Practice 8 2
7. 9x + 12x + 4
2
3
8. 2x + 13x + 18x - 5
719