Name_____________________________________ Class____________________________ Date ________________
Lesson 9-3
Multiplying Binomials
Lesson Objectives
1 Multiply binomials using FOIL
2 Multiply trinomials by binomials
NAEP 2005 Strand: Algebra
Topic: Variables, Expressions, and Operations
Local Standards: ____________________________________
Examples.
1 Multiplying Using FOIL Simplify (4x 2)(3x 6).
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First
(4x 2)(3x 6)
(
Outer
)(3x)
(
Inner
)
(4x)
12x2
Last
( )(3x)
6x
.
3x 2
2 Applying Multiplication of Polynomials Find the area of the
shaded region. Simplify.
(
(
x3
)
area of outer rectangle (3x 2)
x
)
area of hole x
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
)
The product is
(
(2)
2x 1
area of shaded region area of outer rectangle area of hole
(
)
(3x 2)
3x 6x2 2 x2 3x (x 3)
3x Substitute.
Use FOIL to simplify (3x 2)(2x 1)
and the Distributive Property to
simplify x(x 3).
Group like terms.
Simplify.
Quick Check.
1. Simplify each product using FOIL.
a. (3x 4)(2x 5)
c. (3x 4)(2x 5)
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b. (3x 4)(2x 5)
d. (3x 4)(2x 5)
Algebra 1 Lesson 9-3
161
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Example.
3 Multiplying a Trinomial and a Binomial Simplify the product
(3x2 2x 3)(2x 7).
Method 1 Multiply using the vertical method.
3x2
2x
3
2x
7
14x
17x2
Multiply by
.
Multiply by
.
Add like terms.
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4x2
Method 2 Multiply using the horizontal method.
(2x 7)(3x2 2x 3)
(
)(3x2) (2x)(
6x3
The product is
)(
17x2
)(3) (7)(
6x
) ( )(2x) (7)( )
14x
21
.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Quick Check.
2. Find an expression for the area of each shaded region. Simplify.
5x 8
a.
b.
x1
5x
x6
6x 2
x
2x 2
x2
3. Simplify (6n 8)(2n2 n 7) using both methods shown in Example 3.
162
Algebra 1 Lesson 9-3
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