1. ALGEBRA READINESS
Chapter 5 Section 6

2. 5.6: Use the Distributive Property
The parts of an expression that are added together are the terms of the expression.
A term that has no variable part is a constant term.
The number part of a variable part is called the coefficient of the term.
Like terms have the same variable raised to the same power.
You can combine like terms by adding the coefficients of the terms.
Distributive Property
The product of a number and the sum (or difference) of two other numbers is equal to the sum (or difference) of the products of the number and each other.
a(b + c) = ab + ac a(b – c) = ab – ac

3. Identify the property illustrated.
Example 1
Identifying the Properties of Multiplication
Identify the property illustrated.
Statement
Property Illustrated a. 3 1 x • =
Commutative property of multiplication b. 6 5 – ( ) 1 • =
Multiplicative property of – 1
Associative property of multiplication c.
2.7 3 – ( ) • x = d. 7 3 – • =
Multiplicative property of zero

4. Identify the property illustrated.
Example 1
Identifying the Properties of Multiplication
Identify the property illustrated.
Statement
Property Illustrated e. 8 1 • =
Inverse property of multiplication
Identity property of multiplication f.
9.8 • 1 = 4

5. Practice for Example 1
Identify the property illustrated. 1. x – • 1 =
ANSWER
Identity property 2. 3 2 7 5 – • 8 =
ANSWER
Associative property 3. • = ( )
21.5 –
ANSWER
Property of zero

6. Example 2 a. ( ) 5 x – 3.2 = ( ) x 3.2 – 5 = 3.2x – 16 ( ) = 3.2x – 16
Using the Distributive Property a. ( ) 5 x –
3.2 = ( ) x
3.2 – 5
Distributive property =
3.2x – 16 ( )
Multiply. =
3.2x – 16 +
Subtraction rule b. 4 3 – x 2 7 y = 2 7 4 – ( ) x y 3
Distributive property
Multiply. –
14y = 4x 3

7. Practice for Example 2
Use the distributive property to write an equivalent expression. 3. ( )
2.4 + x 3 –
ANSWER
7.2 3x – 4. ( )
12y
16x – 4 3
ANSWER 9y
12x + 5. ( )
2.2
8.7m – 6
ANSWER
13.2
52.2m – 6. w – 2 1 9
ANSWER 19 2w –

8. Practice for Example 2
Use the distributive property to write an equivalent expression. 7. ( ) y 7
0.8 –
ANSWER
0.8y
5.6 + – 8. ( ) 2 + 3z
0.5 –
ANSWER 1
1.5z –

9. Example 3 a. 7x + 5x x = ( ) 5 + 7 = 12x b. 8y 6y + 9 – y = ( ) 8 + 6
Combining Like Terms a. 7x + 5x x = ( ) 5 + 7
Distributive property =
12x
Add. b. 8y 6y + 9 – y = ( ) 8 + 6 9 –
Distributive property = 2y 9 +
Add.

10. Example 4 3 ( ) x 7 – 4x + = 21 – 3x 4x + = 21 4x + ( ) 3x – x = ( ) 4
Simplifying Expressions 3 ( ) x 7 – 4x +
Distributive property = 21 – 3x 4x +
Subtraction rule = 21 4x + ( ) 3x – x = ( ) 4 + 3 –
Distributive property 21
Simplify. = 21 + x 10

11. Practice for Examples 3 and 4
Simplify the expression by combining like terms. 1 3
ANSWER 2 1 r 9. r + r – r 4 4
10. w
1.7w –
3.2w
12.9w
ANSWER
15.4w –

12. Practice for Examples 3 and 4
Simplify the expression.
11. – 5 ( 8x + 2 ) – 3
ANSWER
40x – 13
12. ( ) 10 4r 2 1 r + –
ANSWER 3r – 5