1. ALGEBRA I - SECTION 1-7 (The Distributive Property)@
SECTION 1-7 : THE DISTRIBUTIVE PROPERTY

2. DISTRIBUTIVE PROPERTY : For any numbers, a, b, and c,
a( b + c) = a • b + a • c
TERM : a number, a variable, or the product of a number and a variable.
Examples :
CONSTANT : a term with no variable.
Examples :

3. COEFFICIENT : the number multiplying a variable.
Examples :
SIMILAR (LIKE) TERMS : terms with the same variables with the same exponents.
Examples :
SIMPLEST FORM : an expression written with no grouping symbols and no like terms.
Examples :

4. 6(2x + 5) = 6 • 2x + 6 • 5 = 12x + 30 Simplest Form
Distributive Property
Term
Constant
Coefficient

5. Use the distributive property to simplify each expression.
ANSWER : 4x + 32
2) 5(2n – 7)
ANSWER : 10n - 35
3) -6(4b – 1)
ANSWER : -24b + 6
4) -(6 + a)
ANSWER : a
5) -(2x – 9)
ANSWER : -2x + 9

6. Write each fraction as a sum or difference.
ANSWER : 2x – (13/2)

7. Simplify each expression.
8) 8p – 5p
ANSWER : 3p
9) 10k2 + 6m – 5k + 2m
ANSWER : 10k2 – 5k + 8m
10) 12y – 6 – 15y + 8
ANSWER : -3y + 2
11) 6(3n + 5) + 3n - 50
ANSWER : 21n - 20
12) x3 – 2x2 + 5x + 6x2 – 3x + 1
ANSWER : x3 + 4x2 + 2x + 1

8. Use the distributive property to solve
mentally.
Deli sandwiches cost $4.95 each
including tax. Asa order five deli sandwiches. How much does he owe?
Solution : 5(4.95)
= 5(5 – 0.05)
= 5 • 5 – 5 • 0.05
= 25 – 0.25
= $24.75
14) 199 X 4
ANSWER : 796