# Distributive property

The **distributive property **It is a very deep mathematical principle that helps make mathematics work. It is the rule that allows you to extend the parentheses, so it is very important to understand if you want to be good at simplifying mathematical additions. It is a term widely used in the field of algebra. The distributive property is a property of multiplication that applies to addition and subtraction. This characteristic tells us that two or more terms found in an addition or a subtraction, is equal to the addition or subtraction of the multiplication of each of the terms of the addition or subtraction by the number. To understand the distributive property, we can say that it is a number multiplied by the sum of two addends, which is identical to the sum of the products of each of the addends by that number.

## What is the distributive property?

The **distributive property** is a property of **mathematics** that can be applied to addition and subtraction. It is the multiplication of a number by a **sum** is equal to the sum of the **multiplications** of said number by each of the **addends** .

- What is the distributive property for?
- History
- Distributive property of addition
- Of the division
- Of multiplication
- Filing
- Empowerment
- Examples

## What is the distributive property for?

The **distributive property** of **multiplication** is a very useful property that allows you to **simplify** expressions in which you are multiplying a number by a sum or difference. The distributive property of multiplication over addition can be used when multiplying a number by a sum. The distributive property of multiplication over subtraction is like the distributive property of multiplication over addition. You can **subtract** the numbers and then **multiply them** , or you can **multiply** and then **subtract** . This is known as “spreading the multiplier.”

## History

The **properties** have always been present in the world of **mathematics** , and probably have been used since **ancient times** ; for example, any method of multiplying digit by digit uses the **distributive** property . But it is important to ask ourselves who first recognized these properties globally. So, it is known that the term arose in the early 1800s, when mathematicians began to **analyze** the different types of objects more abstract than numbers, such as **quaternions** and their functions, and needed to talk about what were the **properties of numbers**. These properties were not carefully investigated until mathematics reached a peak in its development, where properties that had previously been assumed had to be clearly spoken in order to make algebra rigorous and allow the study of alternative types of ‘ algebra”.

## Distributive property of addition

It is important to remember that the **sum** is the **combination** of the values of two or more numbers in order to obtain a **total** . The distributive property is one of the mathematical laws related to addition and multiplication and tells us that the sum of two numbers multiplied by a third number is equal to the sum of each addend multiplied by the third number. This property can be represented as follows:

(a + b) xc = (axc) + (bxc)

## Of the division

This property can only be applied in division, only if the algebraic sum is in the dividend and each of the terms that form it are divisible by the divisor. It is very important to note that this mathematical law only takes place within the division if the dividend is first decomposed into equal parts. As a result, all division will lead us to the same quotient, whether it is done directly or by applying the distributive property, it is decided to decompose the dividend into equal parts, in order to divide it each time by the divisor, and then their respective results are added. .

## Of multiplication

The **distributive property** consists of **decomposing** one of the multiplication factors into the addition or subtraction of two others and multiplying each part of this decomposition by the other factor and then adding or subtracting the products, this will allow us to solve mentally and with greater comfort without altering the **result** .

## Filing

When we refer to mathematics, the term **radication** is known as the operation carried out to obtain the **root** of a figure or a number. In other words, radication is the process that, knowing the **index** and the **radicand** , allows us to find the root of a given number. This will be the figure that, when we manage to raise it to the index, will give us the radicand as a result.

## Empowerment

The **enhancement** is a term used when needed raise a number to a given **power** , the operation is performed starting from a **basic** and an **exponent** ; This base raises the exponent.

## Examples

- 8 x (13 – 1) = 8 x 13 – 8 x 1 = 8 x 13 – 8
- 2 x (1 + 3) = 2 x 1 + 2 x 3 = 8
- 10 x (5 – 2) = 10 x 5 – 10 x 2 = 30