11-2 Simplifying Algebraic Expressions
California
Standards
Preview of Grade 7
AF1.3
Simplify numerical expressions by
applying properties of rational
numbers (e.g., identity, inverse,
distributive, associative, and
commutative) and justify the
process used.
Also covered: 6AF1.2, 6AF3.1, 6AF3.2
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
Vocabulary
term
coefficient
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
In the expression 7x + 9y, 7x and 9y are called
terms. A term can be a number, a variable, or a
product of numbers and variables. Terms in an
expression are separated by plus or minus signs.
In the term 7x, 7 is called the
coefficient. A coefficient is a
number that is multiplied by a
variable in an algebraic
expression.
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Coefficient
Variable
11-2 Simplifying Algebraic Expressions
Like terms are terms with the same variable
raised to the same power. The coefficients do
not have to be the same. Constants, like 5, 1
,
2
and 3.2, are also like terms.
Like Terms
Unlike
Terms
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3x and 2x
5x2 and 2x
The exponents
are different
w and w
7
6a and 6b
The variables
are different
5 and 1.8
3.2 and n
Only one term
contains a
variable
11-2 Simplifying Algebraic Expressions
Teacher Example 1: Identifying Like Terms
Identify like terms in the list.
3t
5w2
7t
9v
4w2
8v
Look for like variables with like powers.
3t
5w2
7t
9v
Like terms: 3t and 7t
4w2
8v
5w2 and 4w2
9v and 8v
Helpful Hint
Use different shapes or colors to indicate sets of
like terms.
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
Student Practice 1:
Identify like terms in the list.
2x
4y3
8x
5z
5y3
8z
Look for like variables with like powers.
2x
4y3
8x
5z
Like terms: 2x and 8x
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5y3
8z
4y3 and 5y3
5z and 8z
11-2 Simplifying Algebraic Expressions
To simplify an algebraic expression that contains
like terms, combine like terms. Combining like
terms is like grouping similar objects.
x
x
x
x
4x
+
+
x
x
x
x
5x
x
=
x
x
=
x
x
x
x
x
x
x
9x
To combine like terms that have variables, use the
Distributive Property.
4x + 5x = (4 + 5)x = 9x
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
Teacher Example 2A & 2B: Simplifying Algebraic
Expressions
Simplify. Justify your steps using the
Commutative, Associative, and Distributive
Properties when necessary.
A. 6t – 4t
6t – 4t
6t and 4t are like terms.
2t
Subtract the coefficients.
B. 45x – 37y + 87
In this expression, there are no like terms
to combine.
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
Teacher Example 2C: Simplifying Algebraic
Expressions
Simplify. Justify your steps using the
Commutative, Associative, and Distributive
Properties when necessary.
C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6
3a2 + 5b + 11b2 – 4b + 2a2 – 6
3a2 + 2a2 + 5b – 4b + 11b2 – 6
(3 + 2)a2 + (5 – 4)b + 11b2 – 6
5a2 + b + 11b2 – 6
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Identify like
terms.
Commutative
Property.
Distributive
Property.
11-2 Simplifying Algebraic Expressions
Student Practice 2A & 2B:
Simplify. Justify your steps using the
Commutative, Associative, and Distributive
Properties when necessary.
A. 5y + 3y
5y + 3y
8y
5y and 3y are like terms.
Add the coefficients.
B. 2(x2 – 13x) + 6
2x 2 – 26x + 6
Distributive Property.
There are no like terms to combine.
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
Student Practice 2C:
Simplify. Justify your steps using the
Commutative, Associative, and Distributive
Properties when necessary.
C. 4x2 + 5y + 3x2 – 4y + 2x2 + 5
4x2 + 5y + 3x2 – 4y + 2x2 + 5
Identify like
terms.
4x2 + 3x2 + 2x2 + 5y – 4y + 5
Commutative
Property.
(4 + 3 + 2)x2 + (5 – 4)y + 5
Distributive
Property.
9x2 + y + 5
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
Teacher Example 3: Geometry Application
Write an expression for the perimeter of the
triangle. Then simplify the expression.
2x + 3
3x + 2
x
2x + 3 + 3x + 2 + x
Write an expression using
the side lengths.
(2x + 3x + x) + (3 + 2) Identify and group like
terms.
(2 + 3 + 1)x + (3 + 2) Distributive Property.
6x + 5
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11-2 Simplifying Algebraic Expressions
Student Practice 3:
Write an expression for the perimeter of the
triangle. Then simplify the expression.
2x + 1
2x + 1
x
x + 2x + 1 + 2x + 1
x + 2x + 2x + 1 + 1
(1 + 2 + 2)x + (1 + 1)
5x + 2
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Write an expression using
the side lengths.
Identify and group like
terms.
Distributive Property.
11-2 Simplifying Algebraic Expressions
Lesson Quiz: Part I
Identify like terms in the list.
5n, 8n
1. a5 2a2
a3
3a
4a2
2a2, 4a2
Simplify. Justify your steps using the
Commutative, Associative, and Distributive
Properties when necessary.
2. 4a + 3b + 2a
6a + 3b
9x2 + 2y
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11-2 Simplifying Algebraic Expressions
Lesson Quiz: Part II
3. Write an expression for the perimeter of
the given figure.
2x + 3y
x+y
x+y
2x + 3y
6x + 8y
Holt CA Course 1
11-2 Simplifying Algebraic Expressions
Lesson Quiz: Part I
Identify like terms in the list.
1. 3n2 5n 2n3 8n
2. a5 2a2
a3
3a
5n, 8n
4a2
2a2, 4a2
Simplify. Justify your steps using the
Commutative, Associative, and Distributive
Properties when necessary.
3. 4a + 3b + 2a
6a + 3b
4. x2 + 2y + 8x2
9x2 + 2y
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