12-3 Multiply Rational Expressions
Name
Date
Multiply. Write the product in simplest form.
x2 7x 10 • 6x3 42x2 72x
3x3 15x2 18x
x2 9x 20
(x 2)(x 5)
6x(x 3)(x 4)
•
3x(x 3)(x 2)
(x 5)(x 4)
1
1
2 1
1
Factor the numerators and denominators.
1
( x 2 )( x 5)
(
3)( x 4)
• 6 (x x )(
(
)(
)
3x x3 x2
x 5 x 4)
1 1
1
1
22
1
1
Divide out the common factors; then simplify.
1
simplest form
Multiply. Write the product in simplest form.
2
1. 12a • (8a 40)
3a 15
2
2. 20n • (6n 12)
4n 8
12a2
8a 40
3a 15 •
1
12a2
8(a 5)
3(a 5) •
1
20n2
6(n 2)
•
4(n 2)
1
5 n2
1
4
20 n2
6 ( n 2 )
•
1
(
)
4 n2
32a2
30n2
1
1
1
3
2
22x3
56x •
3. x x x2 2x 63
11x2
Copyright © by William H. Sadlier, Inc. All rights reserved.
1
8 (a 5)
12 a2
•
1
3 ( a 5)
3
3
2
4. 2n 4n 4 96n • 2 15n
n 13n 40
5n
15n3
2n(n 6)(n 8)
•(
n 8)(n 5)
5n4
22x 3
x(x 8)(x 7)
•(
x 7)(x 9)
11x2
1
2
22 x 3
x( x 8 ) ( x 7 )
•(
2
7)( x 9)
x
11x
1
n
1
1
1
2x2(x 8)
x9
6(n 6)
n5
4
3
2
6
5
4
5. 10t 2 9t 9t • 28t 5 26t 4 24t3
4t 12t 9
20t 17t 3t
t 2(5t 3)(2t 3) 2t 4(7t 4)(2t 3)
(2t 3)(2t 3) • t 3(5t 3)(4t 1)
1
1
2t
1
2 t4
6.
9p3 6p2
12p4 64p3 48p2
•
9p2 12p 4
2p2 14p
3p2(3p 2)
4p2(3p 2)(p 6)
•
(3p 2)(3p 2)
2p(p 7)
2p
1
3 p2 (3 p 2)
( 7 t 4 ) ( 2 t 3)
t2 ( 5 t 3 ) ( 2 t 3 )
•
( 2 t 3) ( 2 t 3)
3
(
t 5 t 3 )( 4 t 1)
( 3 p 2) ( 3 p 2)
2t3(7t
6p3(p
1
4)
4t 1
3
15 n3
2 n( n 6) ( n 8)
• (
4
n 8 )( n 5 )
5n
2x
1
1
1
1
1
1
1
•
1
4 p2 ( 3 p 2) ( p 6)
2 p ( p 7)
1
6)
p7
Lesson 12-3, pages 310–311.
Chapter 12 307
For More Practice Go To:
Multiply. Write the product in simplest form.
x2 y2
x y
•
7. 2
x 2 xy y2 2 x 2y
2
n2
8. 3m 3n • m 22mn m n
m n2
3(m n) (m n)(m n)
•
(m n) (m n)(m n)
(x y)(x y) (x y)
(x y)(x y) • 2(x y)
1
1
1
1
3 ( m n) ( m n) ( m n)
•
( m n) ( m n)
( m n)
1 1
2 2
(
)
3( m n)
mn
1
2c
9. 21ab
• 14a4bc3 • 3a
7a3b2
6b7c2
2
1
21a b 14
•
1
7 a3 b2
1 1
10.
bc3
42a2c3
1
b
1
7
42 a2 c3 3 a2 c
•
1
6 b7 c2
21a4c2
b7
1
1
1
n2 2n 1 (n 1)(n 1)
1
1
•
(n 1)
1
n2
2 1 z
x
9xy
z
11. The nth term of sequence A can be
.
represented by the expression 2 1
n 2n 1
The nth term of sequence B is the product
of the nth term of sequence A and n 2 1 .
n
What is the simplest form of the nth term
of sequence B? Write the first four terms
of both sequences.
(n 1) (n 1)
1
15 xy 2
22.5x2y3
6 x 2 y z2
•
3
z
1
4 x z
1
1
22.5 x 2 y 3
2 x3 y
•
z
5 x 4 y 3
c
1
15xy2
2x3y
• 6x2yz2 •
3
4xz
5x4y3
3 x
a 1
a4
1
1
1
1
1
n2(n 1)
1 1 1 1
1 1 1 1
A: , , , ; B: , , ,
4 9 16 25
2 12 36 80
5x 10y 16x2 16xy 4y2
•
.
4x 2y 5x2 20xy 20y2
2(x 2y)
A. 2x y
x
1
1
12. When the length of an edge of a cube is
increased by 8, the ratio of the volumes of the
original to the new cube is a factor of x 8.
What is the other factor? If x 12 cm, what is
the volume of each cube?
Original volume: x3; new volume: (x 8)3
(x 8)4
x3
x3
ratio: (
;
•
(x 8)
x 8)3 (x 8)3
x3
4
(x 8 )
;
So the other factor is
x3
original: 1728 cubic units,
new: 8000 cubic units
13. Multiply
B. 2(2x y)
x 2y
308 Chapter 12
C. (5x 10y)(2x y)
2(x 2y)(x 2y)
D. (x 5y)(2x y)
2(x 2y)(x 2y)
Copyright © by William H. Sadlier, Inc. All rights reserved.
1
( x y ) ( x y ) ( x y )
•
( x y) ( x y) 2 ( x y)