Page 1 of 4
Simplifying Expressions
BEFORE
Now
WHY?
You wrote variable expressions.
You’ll simplify variable
expressions.
So you can simplify a soccer field
expression, as in Ex. 21.
The distributive property can be used to simplify a variable expression:
Word Watch
2x 3x (2 3)x 5x
term, p. 322
like terms, p. 322
equivalent variable
expressions, p. 322
coefficient, p. 322
constant term, p. 322
The parts of an expression that are being added together, such as 2x
and 3x in the expression 2x 3x, are called terms . Terms that have
identical variable parts are like terms . In the expression 2x 3x, 2x
and 3x are like terms. The distributive property allows you to combine
like terms.
EXAMPLE
1
Combining Like Terms
Simplify the expression 7c 9 3c.
7c 9 3c 7c 9 (3c)
with
Solving
After Example 1, the step
of using the distributive
property in order to
combine like terms will
not be shown.
Write expression as a sum.
7c (3c) 9
Commutative property of addition
[7 (3)]c 9
Distributive property
4c 9
Simplify.
In Example 1 above, 7c 9 3c is equivalent to 4c 9. Equivalent
variable expressions are expressions that are equal for every value of
each variable they contain.
The coefficient of a term that has a variable is the number part of the
term. A term that has a number, but no variable, is a constant term . In
the expression 4a 1, 4 is the coefficient of 4a, and 1 is a constant term.
EXAMPLE
2
Coefficients, Constant Terms, Like Terms
Identify the coefficients, constant terms, and like terms of the
expression x 4 2x 10.
First, write the expression as a sum: x 4 (2x) (10).
Coefficient is 1.
Coefficient is 2.
x 4 (2x) (10)
constant terms
322
Chapter 7
Equations, Inequalities, and Functions
x and 2x are like terms.
4 and 10 are like terms.
Page 2 of 4
EXAMPLE
3
Simplifying an Expression
Simplify the expression 5(w 4) w 8.
with
Solving
5(w 4) w 8 5w 20 w 8
Sometimes you need to
use the distributive
property to eliminate
parentheses or brackets
in order to combine like
terms in an expression.
Distributive property
5w (20) w 8
Write as a sum.
5w w (20) 8
Commutative property
6w (12)
Combine like terms.
6w 12
Rewrite without
parentheses.
Your turn now
Identify the coefficients, constant term(s), and like
terms of the expression. Then simplify the expression.
1. 3z 1 4z
Culture
EXAMPLE
4
2. 15 9r 7r 6
3. 2y 4 2y 4
Writing and Simplifying an Expression
Tatami Mats A rectangular tatami
mat is twice as long as it is wide.
Write and simplify an expression for
the perimeter of the mat in terms of
the width w.
2w
w
Solution
Because the mat is twice as long as it is wide, its length is 2w.
Perimeter 2l 2w
■
Formula for perimeter of a rectangle
2(2w) 2w
Substitute 2w for l.
4w 2w
Multiply.
6w
Combine like terms.
Tatami Mats
In Japanese homes, straw
tatami mats are used as
floor coverings. Room sizes
are often measured by the
number of 3 foot by 6 foot
tatami mats that can fit in
the room. What is the area,
in square feet, of a room
that is “five and a half
tatami mats”?
ANSWER An expression for the perimeter of the mat is 6w.
Your turn now
Complete the following exercise.
4. A rectangle is 6 inches longer than it is wide.
Write and simplify an expression for the
perimeter of the rectangle in terms of the width w.
Lesson 7.2
w
w6
Simplifying Expressions
323
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary In the expression 5z 7 2z 1, identify the
coefficients, constant terms, and like terms.
Simplify the expression.
2. 3a 9 a
3. 18 4b 6
4. 8c 4 5
5. Geometry A rectangle is three times longer
w
than it is wide. Write and simplify an expression
for the perimeter of the rectangle in terms of
the width w.
3w
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
9–17, 22–27
6–8
9–17, 22–27
18–21, 29
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Identify the coefficients, constant term(s), and like terms of the
expression.
6. 3x 4 x
7. 10 4y 5y 8
8. 7z 9z 2 z
Simplify the expression.
9. 14t 15 2t
10. 4k 10 7 7k
11. 6 2l 7 3l
12. 10x 4 x 9
13. 14 y y 5
14. p 3 2p 2p
15. 6(1 j) 2j
16. 5(z 2) 8
17. 4b 2 2(b 1)
Geometry Write and simplify an expression for the perimeter of the
rectangle.
18.
19.
20.
2c
3c
z1
x
x 10
3z
21. Soccer A rectangular soccer field is 30 yards longer than it is wide.
Write and simplify an expression for the perimeter of the field in terms
of the width w.
Simplify the expression.
324
Chapter 7
22. m 2 1 2m 1
23. 12v 3(2 4v) 6
24. 2(2t 5 2t) 8t
25. 5 s(4 7) 3s
26. 5 n p 2n 4
27. 5a 2 b 3b 2a
Equations, Inequalities, and Functions
Page 4 of 4
Extended Problem Solving In Exercises 28–30, use the following
information. You have just returned from a 3-day trip. On the first day of
your trip, you took 10 photographs. On the third day of the trip, you took
twice as many photographs as you did on the second day.
28. Write an expression for the number
of photographs you took on each
day. Tell what the variable you
chose represents.
29. Write and simplify an expression
for the total number of
photographs you took.
30. Calculate If you took
12 photographs on the second
day, how many photographs did you take
in all? Explain your reasoning.
Critical Thinking Tell whether the two expressions are equivalent.
31. 13 7t 5;
9t 8 2t
32. 10a 4a 12;
6(a 2)
33. 7x 2x 2;
9x 2
34. Challenge Are the expressions “two more than twice a number”
and “twice the sum of a number and 1” equivalent? Explain.
Mixed Review
Make a box-and-whisker plot of the data. (Lesson 3.4)
35. 26, 55, 14, 25, 35, 40, 28, 43, 44, 25, 18, 21, 42, 38
36. 3, 12, 17, 6, 14, 5, 10, 29, 4, 14, 16
Write a verbal phrase for the variable expression. (Lesson 7.1)
37. p 6
38. 3x 10
39. 2(t 2)
Basic Skills Find the sum.
40. 6.244 0.004
41. 0.9506 1.12
42. 35.008 99.99
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
43. Multiple Choice Which expression is equivalent to 4x 5 6(1 x)?
A. 10x
B. 3x 1
C. 2x 1
D. 5x 5
44. Short Response Write “6 plus twice the sum of a number and 5” as a
variable expression. Then simplify the expression.
Lesson 7.2
Simplifying Expressions
325