Algebra - Distributive Law

over 1 year ago

Hi there. In this math guide, I cover the distributive law from high school algebra. It is assumed that the reader is familiar with working with negative numbers, multiplication and combining like terms.

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Viewing Distributive Law As An Area Of Rectangle

Before getting right into the examples and the algebra I wanted to display the distributive law as an area of a rectangle. This provides a better insight on what the distributive law is doing when working with the algebra. The area of a rectangle is length multiplied by width. If the length and the width are known the area can be determined. If one or both of the length and width are not known we need algebra tools to complete the multiplication. The distributive law is helpful if one of the length or width is known and the other is not known.

This area of a rectangle model is not great if you multiply by a negative number.

Examples

Here are some distributive law examples with picture screenshots.

Example One

What is 7(x + 3)?

Multiply 7 from outside the bracket with the x in the bracket. This gives 7x. Next multiply the seven from the outside with the 3 inside the bracket. This gives 21. The result is 7x + 21.

Example Two

What is 10(2x + y - 3)?

Multiply the ten from the outside of the bracket with 2x then add 10 times y. Watch the negative when multiplying ten with negative 3 to get negative 30.

Example Three

What is -2(x - 3y)?

First multiply negative 2 with x from inside the bracket. The second term would be negative two multiplied by negative 3y. Remember that negative multiplied by a negative gives a positive quantity.

Example Four

Expand -5(3x^2 - 8).

With this one be careful with multiplying negative numbers.

Example Five - Solving An Area Question

The area of a rectangle is 60 square centimetres. Its length is 12 centimeters and the width measure is x + 3 centimetres. What is the value of x and what is the width measure?