7-6 Multiply Polynomials
Name
Date
Use the tabular method to find the product: (x 5)(3x2 5x 1)
3x2
x
3x3
5 15x2
5x
5x2
25x
1
x
5
Multiply the monomials in the rows and columns
to complete the table.
3x3 (5x2 15x2) (25x x) 5
3x3 20x2 24x 5
Find the sum of the monomial terms from the table
by combining like terms.
Simplify.
Multiply: (a2 4)(3a2 4a 7)
(a2 4)(3a2 4a 7) a2(3a2 4a 7) 4(3a2 4a 7)
a2(3a2)
a2(4a)
a2(7)
Apply the Distributive Property.
4(4a) 4(7)
4(3a2)
3a4 4a3 7a2 12a2 16a 28
3a4
4a3
(7a2
12a2)
Simplify.
16a 28
3a4 4a3 19a2 16a 28
Apply the Distributive
Property.
Apply the Commutative
and Associative Properties.
Combine like terms.
So (a2 4)(3a2 4a 7) 3a4 4a3 19a2 16a 28.
Multiply. Use the tabular method. Check students’ tables.
1. (x 4)(4x2 7x 6)
2. (m 6)(3m2 4m 3)
7x
6
x
4x3
7x2
6x
5
20x2 35x 30
3
4x 7x2 6x 20x2 35x 30
4x3 (7x2 20x2) (6x 35x) 30
4x3 27x2 41x 30
3. (4n 3)(5n2 6n 5)
Copyright © by William H. Sadlier, Inc. All rights reserved.
4x2
4. (3y 2)(3y2 5y 6)
3y
2
3y2
9y3
6y2
5y
6
2
15y 18y
10y 12
12c2
5c
7
3m3
18m2
2a2
3a
1
3a2
6a4
9a3
3a2
2a
4a3
6a2
2a
9
108c2
45c
63
4
8a2
12a
4
84c4 13c3 39c2 73c 63
8. (3u 2v)(4u 5v w)
3u
2v
4u
12u2
8uv
5v
15uv
10v2
4n
3
5n2
20n3
6n
24n2
5
20n
15n2
18n
15
20n3 39n2 2n 15
3m3 22m2 27m 18
6a4 13a3 17a2 14a 4
7. (12c2 5c 7)(7c2 4c 9)
4c
48c3
20c2
28c
m
6
4m
3
4m2 3m
24m 18
5. (2a2 3a 1)(3a2 2a 4)
9y3 21y2 8y 12
7c2
84c4
35c3
49c2
3m2
w
3uw
2vw
12u2 23uv 10v2 3uw 2vw
Lesson 7-6, pages 188–189.
6. (4z2 5z 3)(2z2 3z 5)
4z2
5z
3
2z2
8z4
10z3
6z2
3z
12z3
15z2
9z
5
20z2
25z
15
8z4 22z3 41z2 34z 15
9. (16d 2 9d 11)(11d 2 3d 5)
16d 2
9d
11
11d2
176d4
99d3
121d2
3d
48d3
27d2
33d
5
80d2
45d
55
176d4 51d3 68d2 78d 55
Chapter 7
179
For More Practice Go To:
Find the product. Multiply horizontally.
10. (3y2 4)(y2 y 4)
11. (12h2 7)(2h2 3h 13)
12. (b2 1.2b 3.4)(b2 1.5b 2.3)
13. (c2 3.5c 5.2)(c2 1.4c 4.1)
y 4) y 4)
3y2(y2) 3y2(y) 3y2(4) 4(y2) 4(y) 4(4)
3y4 3y3 12y2 4y2 4y 16
3y4 3y3 8y2 4y 16
3y2(y2
4(y2
Find the product. Multiply vertically.
14.
f2 7f 4
f 11
15.
j 2 11 j 6
2j 9
16.
n2 n 6
n2 2 n 3
18.
3 p2 2 p 5
5 p2 7 p 12
19.
7 q2 9 q 12
11q2 7 q 10
f3 7 f2 4 f
11 f 2 77 f 44
f 3 18 f 2 73 f 44
17.
m2 4 m 11
m2 6 m 11
Solve. Show your work.
21. Geometry What is the volume of the right
1
triangular prism? (Hint: Volume 2 area
of base height)
x8
2x 4
x3
x5
Let V volume
V (x 5)(x 3)(x 8)
(x2 2x 15)(x 8)
x3 6x2 31x 120
The volume of the figure
is x3 6x2 31x 120.
22. What are the x- and y-intercepts of
7x 2y 28?
7(0) 2y 28
y 14
7x 2(0) 28
x 4
x-intercept: 4; y-intercept: 14
180
Chapter 7
x
Let V volume
1
x 9 V 2 (2x 4)(x)(x 9)
(x 2)(x)(x 9)
(x2 2x)(x 9)
x3 11x2 18x
The volume of the figure
is x3 11x2 18x.
23. Solve the system of linear equations.
¨2 x 3 y 7 10x 15y 35
9x 15y 3
©
ª«3 x 5 y 1 19x –38; x 2
3(2) 5y 1
5y 5; y 1; (2, 1)
Copyright © by William H. Sadlier, Inc. All rights reserved.
20. Geometry What is the volume of the
rectangular prism? (Hint: Volume length width height)
Answers for Algebra I, Practice Book Lesson 7-6, page 180.
11. 24h4 36h3 156h2 14h2 21h 91
24h4 36h3 142h2 21h 91
12. b44 1.5b33 2.3b22 1.2b3 1.8b2 2.76b 3.4b2 5.1b 7.82
b 2.7b 7.5b 7.86b 7.82
13. c4 1.4c3 4.1c2 3.5c3 4.9c2 14.35c 5.2c2 7.28c 21.32
c4 4.9c3 14.2c2 21.63c 21.32
15. 2 j 3 22 j 2 12 j
9 j 2 99 j 54
2 j3
16.
n4 n3 6 n2
2 n3 2 n2 12 n
3 n2 3 n 18
17.
15 p4 10 p3 25 p2
21p3 14 p2 35 p
36 p2 24 p 60
4
3
15 p 11p 3 p2 59 p 60
19.
180A Chapter 7
m4 4 m3 11m2
6 m3 24 m2 11m2 66 m
44 m 121
m4 2 m3 24 m2 110 m 121
n4 n3 5 n2 15 n 18
18.
31j 2 87 j 54
77 q4 99 q3 132 q2
49 q3 63 q2 70 q2 84 q
90 q 120
77 q4 50 q3 125 q2 174 q 120