- Topics At a Glance
- Arithmetic, Geometric & Exponential Patterns
- Algebraic Expressions
- Evaluating Algebraic Expressions
- Combining Like Terms
**Distributive Property**- Multiplying Monomials
- Multiplying Binomials
- Dividing Polynomials
- Graphing X-Y Points
- Solving One-Step Equations
- Solving Two-Step Equations
- Solving More Complex Equations
- Solving Equations with Variables on Both Sides
- Solving Funky Equations
- Graphing Inequalities
- Solving Inequalities
- Graphing Lines
- Intercepts
- Graphing Horizontal & Vertical Lines
- Graphing Lines By Plotting Points
- Slope-Intercept Form
- Solving Multiple Equations by Graphing

Let's review the properties using variables instead of numbers:

Addition | Multiplication | |
---|---|---|

Commutative | ||

Associative | ||

Inverse | ||

Identity |

The properties above do *NOT work with subtraction and division.*

Here's a handy visual aid on reviewing the properties:

This one is very important when working with algebraic expressions. It basically says this:

and

However, the distributive property does NOT work when the variables inside the parentheses are being multiplied or divided.

and

Let's go through an example very carefully:

By applying the distributive property, we can multiply each term inside the parentheses by 4. This is called "distributing".

Since 12x and 4 are not like terms, this is as far as we can go with the problem.

Well, what about subtraction? Let's look at a subtraction problem using two different methods.

Method 1 Leave as Subtraction | Method 2 Add the Negative |
---|---|

Exercise 1

Use the distributive property to simplify

Exercise 2

Use the distributive property to simplify