Lesson 4-2
Example 1 Identify Like Terms
Identify the like terms in the following expressions.
a. 7y + 1 + 8y
7y and 8y are like terms since the variables are the same.
b. 9a + 2 + 6 + 4a
9a and 4a are like terms since the variables are the same. Constant terms 2 and 6 are also
like terms.
Example 2 Identify Parts of an Expression
Identify the terms, like terms, coefficients, and constants in the expression
x + 5y – 2y – 3.
x + 5y – 2y – 3 = x + 5y + (-2y) + (-3)
= 1x + 5y + (-2y) + (-3)
Definition of subtraction
Identity Property
The terms are x, 5y, -2y, and -3. The like terms are 5y and -2y. The coefficients are 1, 5, and -2.
The constant is -3.
Example 3 Simplify Algebraic Expressions
Simplify each expression.
a. 3x + 9 + 4x
3x + 9 + 4x = 3x + 4x + 9
Commutative Property
= (3 + 4)x + 9
Distributive Property
= 7x + 9
Simplify.
b. 8 – 5m + m – 3
8 – 5m + m – 3 = 8 + (-5m) + m + (-3)
= 8 + (-5m) + (1m) + (-3)
= (-5m) + (1m) + 8 + (-3)
= (-5 + 1)m + 8 + (-3)
= -4m + 5
c. a + 5(2a + 3b)
a + 5(2a + 3b) = a + 5(2a) + 5(3b)
= a + 10a + 15b
= 1a + 10a + 15b
= (1 + 10)a + 15b
= 11a + 15b
Definition of subtraction
Identity Property
Commutative Property
Distributive Property
Simplify.
Distributive Property
Simplify.
Identity Property
Distributive Property
Simplify.
Real-World Example 4
Write and Simplify Algebraic Expressions
AGES Emily and Kate are sisters. Emily is four years younger than Kate. Write an
expression in simplest form that represents the sum of Emily and Kate’s ages.
Words
Emily’s age
Variables
Let x = Kate’s age.
plus
Kate’s age
Let x – 4 = Emily’s age.
Expression
(x – 4) + x = x + (x – 4)
= (x + x) – 4
= (1x + 1x) – 4
= (1 + 1)x – 4
= 2x – 4
(x – 4) + x
Commutative Property
Associative Property
Identity Property
Distributive Property
Simplify.
The expression 2x – 4 represents the sum of Emily and Kate’s ages.