Distributive Law Definition

In Mathematics, distributive law states that the multiplication of a number with a group of numbers gives the same answer if we multiply the same number with the numbers separately and then apply a basic operation on them.

It means if we multiply a particular number with the sum of two numbers, it will give the same answer if we multiply that number with the added numbers separately and add them in the end. Let us show you the general form of distributive law for better understanding.


You can read about Associative Law here.

General form of Distributive Law

A (B + C) = AB + AC

In the above general form, A, B, and C represents numbers. Here we are going to show you a quick example to understand it properly.

Example 1:

Solve the following expression using the distributive law to check if the law holds or not.

3 (20 + 4)


Let us first solve the expression by adding the terms given in the bracket.

= 3 (24)
 = 72

Now, let’s multiply 3 with the numbers given in the bracket one by one.

= 3(20) + 3(4)
= 60 + 12
= 72

As we have got the same answer in both formats, it means that the distributive law holds on this expression.

Types of Distributive Law

On the basis of basic mathematical operations, distributive law has two main types. Let us discuss them one by one here quickly.

• Distributive law over addition

In this type, the distributive law holds when the terms are added and then multiplied by a single number.


You can read about Term here.

Example 2:

Solve the expression using distributive law:

12 (3 + 7)


= 12 (21)
= 252

As it is clear that the terms are added first and then multiplied by the final number. It shows the general solution of distributive law over addition. We can also multiply the external term with the inner terms one by one and add them like we have done in Example 1.

• Distributive law over subtraction

This distributive law holds when two terms are subtracted along with the multiplication of the final term. In simple words, the terms are subtracted from each other and then multiplied by the given external number.

Example 3:

Solve the expression using distributive law:

4 (23 - 2)


= 4 (21)
= 84

To solve the above expression, we can also multiply the external term with the inner terms one by one. In the end, we have to subtract the answers to reach the final answer.


What is the general formula of distributive law?

The general formula of distributive law is given by:

A (B + C) = AB + AC

What does distributive mean in Mathematics?

Distributive means sharing or division. It means to divide a single term into two or more parts.

Does distributive law apply to addition?

Yes, distributive law applies to addition and subtraction both.