Page 742 - Basic College Mathematics with Early Integers

718 A PPEND I X B I EXPONENTS AND POLYNOMIALS

Objective Multiplying Binomials

Recall from Appendix B.1 that a polynomial that consists of exactly two terms is called
a binomial. To multiply two binomials, we use a version of the distributive property:
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1b + c2a = b a + c a
PRACTICE 3 Example 3 Multiply: 1x + 221x + 32

Multiply: 1b + 721b + 52
Solution:

(x+2)(x+3)=x(x+3)+2(x+3) Apply the distributive property.
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=x x+x 3+2 x+2 3 Apply the distributive property.
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=x +3x+2x+6 Multiply.
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=x +5x+6 Combine like terms.
Work Practice 3
PRACTICE 4 Example 4 Multiply: 14y + 9213y - 22
Multiply: 15x - 1215x + 42
Solution:

(4y+9)(3y-2)=4y(3y-2)+9(3y-2) Apply the distributive
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=4y 3y+4y(–2)+9 3y+9(–2) Apply the distributive
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=12y -8y+27y-18 property.
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=12y +19y-18 Multiply.
Combine like terms
Work Practice 4
Objective Squaring a Binomial

Raising a binomial to the power of 2 is also called squaring a binomial. To square a
binomial, we use the definition of an exponent, and then multiply.

PRACTICE 5 Example 5 Multiply: 12x + 12 2
Multiply: 16y - 12 2
Solution:

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(2x+1) =(2x+1)(2x+1) Apply the definition of an exponent.
=2x(2x+1)+1(2x+1) Apply the distributive property.
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=2x 2x+2x 1+1 2x+1 1 Apply the distributive property.
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=4x +2x+2x+1 Multiply.
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=4x +4x+1 Combine like terms.
Work Practice 5
Objective Using the FOIL Order to Multiply Binomials

Recall from Example 3 that
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1x + 221x + 32 = x x + x 3 + 2 x + 2 3 Copyright 2012 Pearson Education, Inc.
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= x + 5x + 6
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Answers One way to remember these products—x x, x 3, 2 x, and 2 3 —is to use a special
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3. b + 12b + 35 4. 25x + 15x - 4 order for multiplying binomials, called the FOIL order. Of course, the product is the
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5. 36y - 12y + 1 same no matter what order or method you choose to use.