Lesson 2.5
Core Focus on
Introductory Algebra
Simplifying Algebraic Expressions
Warm-Up
Evaluate each expression when x = 5.
1. 4x + 7
27
6x
2.
10
3
3. x2 − 11
14
4. 5(x + 3)
40
Lesson 2.5
Simplifying Algebraic
Expressions
Recognize and combine like terms
to simplify algebraic expressions.
Vocabulary
Term
A number or a product of a
number and a variable.
Coefficient
The number multiplied by a
variable in a term.
Constant
A term with no variable.
Like Terms
Terms that have the same variable.
3x and 7 are terms
3x + 7
expression
7 is also called a
constant
Example 1
x can also be
written 1x
Match pairs of like terms.
6x
2y
3m
x
9
3m
5
14y
There are four pairs of like terms. Each pair of like terms
has the same variable or no variable.
6x and x
9 and 5
2y and 14y
3m and 3m
Good to Know!
In order to simplify an algebraic expression you must combine like
terms.
When combining like terms you must remember that the operation
in front of the term (addition or subtraction) must stay attached to
the term.
Rewrite the expression by grouping like terms together before
adding or subtracting the coefficients to simplify.
Example 2
Simplify each algebraic expression by combining like terms.
a. 4x + 3x + 5x
All terms are alike so add the
coefficients together.
4x + 3x + 5x = 12x
4x + 3x + 5x = 12x
Example 2 Continued…
Simplify each algebraic expression by combining like terms.
b. 8y + 6 + 3 + 4y + 1
There are two types of like terms
in this expression: constants and
terms that have the y variable.
8y + 6 + 3 + 4y + 1
8y + 4y + 6 + 3 + 1
Rewrite the expression so the like
terms are next to each other.
12y
Add the coefficients of the like
terms together.
8y + 6 + 3 + 4y + 1 = 12y + 10
+
10
Example 2 Continued…
Simplify each algebraic expression by combining like terms.
c. 9m + 10p − 3p − 2m + 4m
Group the like terms together.
The addition or subtraction sign
must stay attached to the term.
9m + 10p − 3p − 2m + 4m
9m − 2m + 4m + 10p − 3p
Add or subtract the coefficients
of the like terms from left to right.
11m
9m + 10p − 3p − 2m + 4m = 11m + 7p
7p
Example 2 Continued…
Simplify each algebraic expression by combining like terms.
d. 4d + 12 + d − 12
Group like terms together.
If a variable does not have a
coefficient written in front
of it, then the coefficient is 1.
Add or subtract the coefficients
of the like terms.
4d + 12 + d − 12 = 5d
4d + 12 + d − 12
4d + d + 12 − 12
5d + 0 = 5d
Zero does not need
to be written.
Communication Prompt
Write a few sentences about simplifying expressions.
Use the vocabulary words listed below in your
sentences.
Term
Constant
Like terms
Coefficient
Exit Problems
Simplify each expression.
1. 3y + 2y + 8y
13y
2. 9x + 8w − 2x + w
7x + 9w
3. 3m + 4m + 5 + 1 − 7m
6