explain about distributive property under intersection
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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.
Distributive Property Definition
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:
A ( B+ C) = AB + AC
Where A, B and C are three different values.
Let’s consider a simple example: 2(4 + 3).
Since the binomial “4 + 3” is in the parenthesis, according to the order of operations, you have to calculate the value of 4 + 3 and then multiply it by 2, which gives the resultant value as 14.
Distributive Property
Distributive Property with Variables
Consider an example here: 6(2+4x)
The two values inside the parenthesis cannot be added since they are not like terms, therefore it cannot be simplified any further. We need a different method and this is where Distributive Property can be applied.
If you apply Distributive Property,
6× 2 + 6 × 4x
The parenthesis no longer exists and every term is multiplied by 6.
Now, you can simplify the multiplication for individual terms.
12 + 24x
The distributive property of multiplication lets you simplify expressions wherein you multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products. In algebra, we can have the distributive property for two arithmetic operations such as:
Distributive Property of Multiplication
Distributive Property of Division