How to Apply the Distributive Property

Once you learn the distributive property, you'll apply it throughout the rest of your math career. The rule teaches you how to distribute terms in math expressions properly. Once you master it, you will find it easier to simplify and solve complex algebra problems, regardless of whether they involve numbers, variables or exponents.

Difficulty:

Moderately Easy

Instructions

1. Understand what the distributive property says: You can multiply each term of an expression in parentheses by the same factor and get the same answer as you would if you had solved the expression within the parentheses first and then multiplied the result by the factor.

   From a formula perspective, the distributive property is easy to remember. If you're given a(b + c), you distribute the "a" to both the "b" and "c" terms to get a * b + a * c.

2. Solve an example problem to show how the distributive property works: For example, consider the following expression: 7(x - 3) To simplify this expression, distribute the "7" to both the "x" and the "3." The new expression look like this: 7 * x - 7 * 3 Then further simplify the expression to 7x - 21.

3. Use caution when the number you're distributing is negative. In that case, the signs of the other numbers will change. For example, suppose you're given the expression -7(x - 3). When you distribute the -7, the new expression will look like this:

   -7 * x - (-7) * 3 or -7x - (-21)

   This simplifies to -7x + 21.

References

• Purplemath: Basic Number Properties: Associative, Commutative and Distributive