Page 19 - Math Course 2 (Book 1)

Using the Distributive Property

Let’s Begin Simplify 6x + 4 – 5x – 7.
6x and –5x are like terms. 4 and –7 are also like
terms.

6x + 4 – 5x – 7 = 6x + 4 + (–5x) + (–7)
Identify Parts of Expressions Def nition of subtraction

= 6x + (–5x) + 4 + (–7)
Example Commutative Property
= [6 + (–5)]x + 4 + (–7)
Identify the terms, like terms, coef cients, and Distributive Property
constants in the expression 4x – x + 2y – 3.
= x –3 Simplify
4x – x + 2y – 3 = 4x + (–x) + 2y + (–3)
Def nition of subtraction.
Answer x – 3
= 4x + (–1x) + 2y + (–3)
Identity Property.

The terms are 4x, –x, 2y, and –3. Simplify –y + 2(x + 3y).
The like terms are 4x and –x. The
Answer
coef cients are 4, –1, and 2. The –y + 2(x + 3y) = –y + 2x + 2(3y) Distributive Property
constant is –3.
= –y + 2x + 6y Associative Property

= –1y + 6y + 2x Commutative
Property
Simplify Algebraic Expressions
= (–1 + 6)y + 2x Distributive Property
Example = 5y + 2x Simplify

Simplify 8n + 4 + 4n. Answer 5y + 2x
8n and 4n are like terms.

8n + 4 + 4n = 8n + 4n + 4 Commutative
Property Real World Example

= (8 + 4)n + 4 Distributive WORK
Property
You and a friend worked in the school store last
week. You worked 4 hours more than your friend.
= 12n + 4 Simplify.
Write an expression in simplest form that represents
the total number of hours you both worked.
Answer 12n + 4 Words number of hours your friend worked

+ number of hours you worked

Variables Let h = number of hours your friend
worked.
Let h + 4 = number of hours you
worked.

Expression h + h + 4

11