Understanding the Distributive Laws of Multiplication | Simplify and Solve Equations

Distributive laws

The distributive laws are a set of mathematical rules that explain how multiplication or division can be distributed over addition or subtraction operations

The distributive laws are a set of mathematical rules that explain how multiplication or division can be distributed over addition or subtraction operations. There are two distributive laws: the distributive law of multiplication over addition and the distributive law of multiplication over subtraction.

1. Distributive Law of Multiplication over Addition:
The first distributive law states that when we multiply a number (or term) by the sum of two or more other numbers (or terms), we can distribute the multiplication individually to each term and then add the results. Mathematically, this can be expressed as:

a * (b + c) = (a * b) + (a * c)

Here ‘a’ is a number that is multiplied, and ‘b’ and ‘c’ are the terms being added.

For example, let’s say we have the expression 3 * (2 + 4). We can apply the distributive law of multiplication over addition to this expression as follows:

3 * (2 + 4) = (3 * 2) + (3 * 4)
= 6 + 12
= 18

2. Distributive Law of Multiplication over Subtraction:
The second distributive law states that when we multiply a number (or term) by the difference of two other numbers (or terms), we can distribute the multiplication individually to each term and then subtract the results. Mathematically, this can be expressed as:

a * (b – c) = (a * b) – (a * c)

Here ‘a’ is a number that is multiplied, and ‘b’ and ‘c’ are the terms being subtracted.

For example, let’s say we have the expression 4 * (6 – 3). We can apply the distributive law of multiplication over subtraction to this expression as follows:

4 * (6 – 3) = (4 * 6) – (4 * 3)
= 24 – 12
= 12

Both distributive laws are fundamental principles in algebra and are widely used in simplifying expressions, expanding brackets, and solving equations. They allow us to break down complex expressions into simpler ones, making calculations easier.

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