This property is one that you will use all the time! It deals with multiplying a group of terms that are together in a parenthesis by a common number or term. It’s best taught by looking at examples.

Example 1:

\(4(3x + 2)\)       We have to multiply both terms in the parenthesis by the 4 and add our answers.

\(4(3x + 2)\)
\(4(3x) + 4(2)\)
\(12x + 8\)

Example 2:

\( - 5x(2x - 8)\)    Be careful with your exponents and your signs!

\( - 5x(2x - 8)\)
\( - 5x(2x) +  - 5x( - 8)\)
\( - 10{x^2} + 40x\)

Sometimes the distributive property must be used within an equation. Make sure you can recognize which term to distribute.

Example 3:

\(7x + 6(6 - x)\)    We are distributing the 6 into (6 – x).

\(7x + 6(6) + 6( - x)\)
\(7x + 36 - 6x\)

Now, combine like terms. 7x and -6x equals 1x or just x.

\(x + 36\)

Example 4:

\( - 4b - 4(7b + 1)\)        We are actually distributing a -4 into the parenthesis. I would rewrite it like this.

\( - 4b +  - 4(7b + 1)\)    Now, use the distributive property.

\( - 4b +  - 4(7b) +  - 4(1)\)
\( - 4b - 28b - 4\)

Combine like terms. -4b and -28b combine to become -32b.

\( - 32b - 4\)

Below you can download some free math worksheets and practice.