Distributive property examples

Oct 20, 2021, 16:45 IST

Distributive property and Its examples

Distributive property explains that the operation performed on numbers, available in brackets that can be distributed for each number outside the bracket. It is one of the most frequently used properties in Maths. The other two major properties are commutative and associative property.

The distributive property is easy to remember. There are a number of properties in Maths which will help us to simplify not only arithmetical calculations but also the algebraic expressions. In this article, you will learn what is distributive property, formula, and solved examples.

Table of Content for Distributive property examples

i. Introduction to Distributive Property

ii. Distributive Property Defination

iii. Distributive Property with Variables

IV. Distributive Property of Multiplication

V. Distributive Property of Multiplication over Addition

VI. Distributive Property of Multiplication over Subtraction

VII. Distributive Property of Division

VIII. Examples

Distributive Property Defination

The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation. This property can be stated symbolically as:

X(y +z) = x y + x z

Where x, y, and z are three different value

Let assume an example:

3(4 + 6)

Since the binomial “4 + 6” is in the parenthesis, according to the order of operations, you have to calculate the value of 4 + 6 and then multiply it by 3, which gives the resultant value as 30.

Distributive Property with Variables

Let us assume an example: 6(2 + 3x)

The two values inside the parenthesis can't be added since they're not like terms, therefore it can't be simplified any longer. we'd like a special method and are often. This is often where Distributive Property can be applied.

If you apply Distributive Property,

6 x 2 + 6 x 3x

The parenthesis no longer exists and every term is multiplied by 6.

Now, you can simplify the multiplication for individual terms.

12 + 18x

The distributive property of multiplication allows you to simplify expressions wherein you multiply variety by a sum or difference. consistent with this property, the merchandise of a sum or difference of variety is adequate to the sum or difference of the products. In algebra, we will have the distributive property for 2 arithmetic operations like:

i. Distributive Property of Multiplication

ii. Distributive Property of Division

Distributive Property of Multiplication

The distributive property of multiplication are often expressed under addition and subtraction. meaning, the operation exists inside the bracket, i.e. between the numbers inside the bracket are going to be addition or subtraction. Let’s understand these properties with the examples here.

Distributive Property of Multiplication Over Addition

The distributive property of multiplication over addition is applied once you multiply a worth by a sum.

For example, you want to multiply 3 by the sum of 2 + 3.

As we have like terms, we usually first add the numbers and then multiply by 3.

3(2 + 3) = 3(5) = 15

According to the property, you can first multiply every addend by 3. This is known as distributing the 3 and then you can add the products.

The multiplication of 3(2) and 3(3) will be performed before you add.

3(2) + 3(3) = 6 + 9 = 15

You can note that the result is the same as before.

You probably use this method without actually knowing that you simply are using it

The below equations describe both the methods. We've 2 and 3 on the left-hand side then multiplied by 2. This expansion is rewritten by applying the distributive property on the right-hand side where we distribute 5 then multiply by 2 and add the results. You'll see that the result's similar in each case.

3(2 + 3) = 3(2) + 3(3)

3(5) = 6 + 9

15 = 15

Distributive Property of Multiplication over Subtraction

Now, let’s have a look at the example of a distributive property of multiplication over subtraction.

Suppose we have to multiply 6 with subtraction of 18 and 4, i.e. (18 – 4).

This can be performed in two ways.

Case 1: 6 × (10 –4) = 6 × 6 = 36

Case 2: 6 × (10 – 4) = (6 × 10) – (6 × 4) = 60 – 24 = 36

Whichever is that the procedure, the ultimate result is going to be an equivalent in both cases. The distributive properties of addition and subtraction are often utilized to rewrite expressions for various purposes. Once you multiply variety by a sum, you'll add and multiply. Also, you'll first multiply each addend then add the products. This is applicable to subtraction also. In every case, you disturb the outer multiplier to each value within the parenthesis, in order that multiplication occurs with every value before addition or subtraction.

Distributive Property of Division

We can divide larger numbers using the distributive property by breaking those numbers into smaller factors.

Let us see an example here:

Q: Divide 36 ÷ 6.

We can write 36 as 18+18

Hence,

(18 + 18) ÷ 6

Now distributing division operation for every think about the bracket we get;

(18 ÷ 6) + (18 ÷ 6)

= 3 + 3

= 6

Examples

Example 1:

Solve the given expression using the distributive property:

(i) 2(3x⁴+ 7x)

(ii) 3x(x²+ y)

(iii) 4(2xy+ 5yx)

Solution:

According to the distributive property,

A ( B + C) = AB + AC

(i) 4(2x⁴+ 7x)

Using distributive law we have,

= 2. 3x⁴+ 2. 7x

= 6x⁴+ 14x

(ii) 3x(x²+ y)

Using Distributive property,

= 3x .  x²  +3x . y

= 3x³+ 3xy

(iii) 4(2xy+ 5yx)

Using distributive property, we have

= 4. 2xy + 4. 5yx

= 8 xy + 20 xy

= 28 xy