1. The Distributive Property
Chapter 2 Section 4
The Distributive Property

2. a(b + c) = ab + ac (b + c)a = ab + ac a(b – c) = ab – ac (b – c)a
Distributive Property
For all real numbers (rational and irrational) a, b and c
a(b + c)
= ab + ac
(b + c)a
= ab + ac
a(b – c)
= ab – ac
(b – c)a
= ab – ac
Distribute means to spread or share evenly.

3. Simplifying an Expression
Examples
= a ∙ 4 – 6 ∙ 4
= 4a – 24
4(a – 6) 1
= 6x + 9 2
(5y – 3)(2)
= 5y(2) – 3 (2)
= 10y – 6 3

4. Using the Multiplication Property of -12
-4(m – 3)
= m ∙ -4 – 3 ∙ -4
= -4m + 12

5. Solve using the distributive property1
4(2 + n) = 24
b – (6b + 3) = -6 2
8 + 4n = 24
b – 6b – 3 = -6
4n + 8 = 24
– – 8
4n = 16
n = 4
-5b – 3 = -6
-5b = -3
-5 -5
b =

6. Algebraic Expression Number of Terms
In an algebraic expression, a term is a number, a variable, or the product of a number and one or more variables.
Algebraic Expression
Number of Terms
3x + 2 2
7xy + 9x – 15 3
6a2 – 5ab + 3b – 12 4
A constant is a term that has no variable.

7. Term Coefficient 3X 3 – X – 1 7y 7 Example
If a term has a variable, the numerical factor is called the coefficient.
Example
Term
Coefficient 3X 3
– X
– 1 7y 7

8. Like Terms Unlike Terms
Like Terms are terms that have exactly the same variable factors + exponents.
Example
Like Terms 3X 7X
4ab
- 3ab
5x2y
9x2y
Unlike Terms 3 4z
7ac
6bc
- 2a2b3
- 4a2b4

9. Combining like terms is one way of simplifying an expression.
Example
2 + 6x + z – 2x + 8 – 4z
like terms
6x - 2x 4x
z - 4z - 3z
4x – 3z + 6
variables are arranged in alphabetical order

10. Assignments
Class Work
Page 82 – 83 #15 – 45 odd
#53 – 61 odd #
#65 – 75 odd
#76 & 77
Challenge: #
Homework
Page 85 #