### The Distributive Property

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.

$$- 32b - 4$$

9258 x

Simplify each expression.

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4380 x

Simplify each expression.

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2722 x

Simplify each expression.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

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