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Lesson 7.3 Simplifying Algebraic Expressions
Simplify each expression. Then write the coefficient of the variable in the expression.
Example
s1s1s5
5
5
5s
In the term
5s
s
61616536
s1s1s53s
3  s is the same as 3s.
, the coefficient of s is
1. p 1 p 1 p 1 p 1 p 1 p 5
5
.
p
5
In the term
, the coefficient of p is
2. n 1 n 1 n 1 13 1 8 5
 n 1 13 1 8
1 21
5
In the term
, the coefficient of n is
3. d 1 d 1 d 1 d 1 d 1 5 2 2 5
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5
In the term
13
.
1 11
, the coefficient of m is
5. r 1 r 1 r 1 r 1 r 1 15 2 5 5
In the term
.
d1522
, the coefficient of d is
4. m 1 m 1 m 1 m 1 3 1 8 5
In the term
.
.
1 10
, the coefficient of r is
.
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Solve.
Example
A square has a length of g yards.
Find the perimeter of the square in terms of g.
g yd
?
g yd
yd
4
g1g1g1g5
yd
yd
2121212542
g1g1g1g54g
4  g is the same as 4g.
g
4g
5
The perimeter of the square is
4g
yards.
6. An equilateral triangle has sides measuring d inches long.
Find the perimeter of the equilateral triangle in terms of d.
d in.
?
1
in.
in.
1
5

5
The perimeter of the triangle is
188
inches.
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d in.
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7. A rectangle has a width of 2 feet and a length of m feet.
Find the perimeter of the rectangle in terms of m.
m ft
2 ft
?
m ft
2 ft
ft
1
1
1
5
ft

1
5
The perimeter of the rectangle is
feet.
8. A piece of wire is bent in the shape a regular octagon.
Each side of the octagon is h centimeters long.
What is the total length of the wire in terms of h?
h cm
?
h cm
cm
cm
cm
cm
cm
cm
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cm
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Simplify each expression.
Example
Simplify 2c 1 3c.
2c
c
3c
c
c
c
c
2c 1 3c 5 c 1 c 1 c 1 c 1 c
5
2c 1 3c and 5c are equivalent expressions
because they are equal for all values of c.
If c 5 1, 2c 1 3c 5 5 and 5c 5 5.
If c 5 2, 2c 1 3c 5 10 and 5c 5 10.
5c
9. 3g 1 4g 5
?
g
3g
g
g
g
g
g
4g
10. 8p 1 3p 5
11. 6m 1 10m 5
12. 16y 1 4y 5
13. 42d 1 d 5
State whether each pair of expressions is equivalent.
14. 7p 1 2p and 3p 1 6p
15. 9r 1 3r and 5r 1 3r
16. 6m 1 m and 8m
17. 8y 1 4y and 12y
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g
Chapter 7 Lesson 7.3
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Simplify each expression.
Example
5t 2 2t
5t
t
t
t
t
t
2t
5t 2 2t 5
5t 2 2t and 3t are equivalent expressions
because they are equal for all values of t.
If t 5 3, 5t 2 2t 5 9 and 3t 5 9.
If t 5 4, 5t 2 2t 5 12 and 3t 5 12.
3t
18. 7x 2 4x 5
7x
x
x
x
x
x
x
x
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4x
19. 18n 2 2n 5
20. 6g 2 6g 5
21. 44z 2 15z 5
22. 15b 2 b 5
State whether each pair of expressions is equivalent.
23. 5n 2 n and 6n
24. 4e 2 4e and 10w 2 10w
25. 7a 2 2a and 9a 2 4a
26. 9u and 12u 2 2u
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Simplify each expression.
Example
7v 2 3v 1 2v 5
4v
5
6v
1 2v
27. 12c 2 3c 2 3c
28. 5j 1 2j 1 9j
2 3c
5
When adding and subtracting
algebraic expressions with
no parentheses, always work
from left to right.
5
1 9j
5
5
29. 9k 1 3k 2 2k
30. 8y 2 5y 1 2y
Example
8 1 5g 2 2 1 6g
192
5
5 g 1 6g
5
11g 1 6
1
822
First, identify like terms. Then
change the order of terms to
collect like terms. Lastly, simplify.
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Simplify each expression.
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31. 5t 1 4 1 2t
32. 6m 2 10 2 2m 2 m
1
5
5
5
1
5
33. 7r 1 5r 2 12
34. 8 1 3j 2 5 2 2j 1 8j
Solve.
Example
The figure shows an isosceles triangle. Find the perimeter of the triangle.
5
5w 1 1
1
5w 1 1
5
5w 1 5w 1 4w
1
111
5
14w 1 2
1
4w
(5w 1) yd
4w yd
The perimeter of the triangle is
(14w 1 2)
yards.
35. The figure shows a rectangle. Find the perimeter of the rectangle.
1
1
1
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5y cm
5
1
5
The perimeter of the triangle is
(2y 2) cm
centimeters.
36. The figure shows a trapezoid. Find the perimeter of the trapezoid.
(17 d) in.
(d 8) in.
5d in.
11 in.
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Lesson 7.4 Expanding and Factoring Algebraic Expressions
Expand each expression.
Example
3(f 1 2)
3(f 1 2) means 3 groups of (f 1 2):
f
f
2
f
2
3(f 1 2) is the same as 3  (f 1 2).
3  (f 1 2)
5 (f 1 2) 1 (f 1 2) 1 (f 1 2)
5f1f1f121212
5 3f 1 6
2
1 group
f
f
f
2
2
2
32
3f
3(f 1 2) 5 3  (f 1 2)
5
3f
5
3f 1 6
32
1
1. 4(g 1 4)
g
g
4
g
4
g
4
4
g
g
g
g
4

5
194
4

4(g 1 4) 5 4  (g 1 4)
5
4
1
4
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1 group
Chapter 7 Lesson 7.4
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2. 2(h 1 7)
3. 9(k 2 4)
4. 6(7s 1 9)
5. 3(9c 2 6)
State whether each pair of expressions is equivalent.
6. 6(2u 1 3) and 6u 1 18
7. 3(2h 2 5) and 6h 2 15
8. 8(g 1 2) and 16 1 8g
9. 7(2k 2 4) and 28 2 14k
Factor each expression.
Example
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4y 1 2
The factors of 4y are:
The factors of 2 are:
1  4y
12
2
2y
4
1y
To factor an expression,
look for common factors in
the terms of the expression.
The common factor of 4y and 2 is
2
4y 5
25
2
4y 1 2 5
5

2
.
2

2y

1
2

2y
1
1
2(2y 1 1)
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10. 3d 1 9
The factors of 3d are:
The factors of 9 are:
1  3d
19
3 
3
9
The common factor of 3d and 9 is
3d 5
.

95

3d 1 9 5

1

11. 24g 1 8
12. 21b 2 7
13. 45h 1 5
14. 54z 2 6
State whether each pair of expressions is equivalent.
15. 22s 1 18 and 2(11s 1 9)
16. 6h 1 15 and 3(2h 2 5)
17. 20p 1 14 and 4(5p 1 3)
18. 15f 2 9 and 5(3f 2 9)
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Chapter 7 Lesson 7.4
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Simplify each expression. Then factor the expression.
Example
9m 1 19 1 4m 1 7
5
9m
1
4m
5
13m
1
26
5
1
19
1
7
Identify like terms. Change the order
of terms to collect like terms.
Simplify.
13(m 1 2)
Factor.
19. 6p 1 2 1 4p 1 13
5
1
5
1
5
1
1
Identify like terms. Change the order
of terms to collect like terms.
Simplify.
Factor.
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20. 2v 1 11 1 3 1 5v
21. 9(6a 1 7) 2 6 2 3a
22. 6(3 1 2s) 1 4(s 1 8)
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