# Using the Distributive Property to Expand Algebraic Expressions

In this lesson, we will be using the distributive property to expand algebraic expressions. Algebra tiles are used to show the concepts involved.

Two more examples of how to expand a problem using the distributive property.

This video uses the distributive property to create equivalent fractions and then gives two examples of how this can be helpful when simplifying expressions.

### Review:

Distributive Property of Multiplication Over Addition
states that a product can be found by adding, then multiplying, or by multiplying, then adding.
Example 1

 $3 * (10 + 4)$ $=$ $(3 * 10) + (3 * 4)$ $3 * (13)$ $=$ $(30) + (12)$ $42$ $=$ $42$

Example 2

 $3 * (n + x)$ $=$ $(3 * n) + (3 * x)$ $3(n + x)$ $=$ $(3n) + (3x)$

#### Try these four problems:

Fill in the blanks:
1.    $7(5+3)=$______ $+$______
2.    $6a+6b=$______$(a+b)$

Simplify the expressions:
3.    $2x + 3(x-4 + 2x) + (2-2x)$

4.    $\frac{x + 1}{5n} + \frac{4-2x}{5n}$

 1. Original problem: $7(5+3)=$____ $+$____ a. Distribute the 7 $7(5+3)=$ $7*5$$+$$7*3$ ………………………………….. ……………………………. 2. Original problem: $6a+6b=$______$(a+b)$ a. Factor out the 6 $6a+6b=$ $6$$(a+b) ………………………………….. ……………………………. 3. Original problem: 2x + 3($$x$$- 4 +$$2x$$) + (2-2x) a. Simplify what we can in the parentheses 2x+\color{#f15a23}{3(}\color{blue}{3x}-4\color{#f15a23})\color{#4a4949″}{+(2-2x)} b. Use the distributive property to remove the parentheses 2x +$$9x-12$$-4 + 2-2x c. Combine like terms \color{blue}{2x + 9x}$$- 12 + 2$$-2x$ d. Solution $\color{red}{9x-10}$ ………………………………….. ……………………………. 4. Original problem: $\dfrac{x + 1}{5n} + \dfrac{4-2x}{5n}$ a. Since the fractions have a common denominator we can add them. $\dfrac{(x + 1) + (4-2x)}{5n}$ b. Rearrange the terms. $\dfrac{(x + ^-2x) + (1+4)}{5n}$ c. Now we can combine like terms $\color{red}{\dfrac{5-x}{5n}}$