Distributive property

The property of distributing the multiplication across the addition or subtraction of the terms is called the distributive property.

Introduction

$a$, $b$ and $c$ are three literals but represent three terms in algebraic form. The sum and difference of the terms $b$ and $c$ are written as $b+c$ and $b-c$ respectively. The distributive property can be written in terms $a$, $b$ and $c$ in two different forms.

Addition form

$a(b+c) \,=\, ab+ac$

Learn how to distribute the multiplication over addition.

Subtraction form

$a(b-c) \,=\, ab-ac$

Learn how to distribute the multiplication over subtraction.

Usage

The distributive property is mainly used in two different cases.

1. To distribute the multiplication across the sum or difference of the terms.
2. To take the common factor out from the sum or difference of the terms.