Mastering the Distributive Property in Algebra | Simplify and Manipulate Expressions

distributive property

The distributive property is one of the fundamental properties in algebra that allows us to simplify and manipulate expressions

The distributive property is one of the fundamental properties in algebra that allows us to simplify and manipulate expressions. It states that for any real numbers a, b, and c, the product of a and the sum (or difference) of b and c is equal to the sum (or difference) of the products of a and b, and a and c.

Mathematically, the distributive property can be written as:

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

or

a * (b – c) = a * b – a * c

In simpler terms, if we have a number multiplied by a sum (or difference) of two terms, we can distribute that number to each term individually by multiplying it with each term, and then add (or subtract) the results.

Let’s look at an example to illustrate the distributive property:

Example: Simplify the expression 3 * (2 + 5)

Using the distributive property, we have:

3 * (2 + 5) = 3 * 2 + 3 * 5

Simplifying further:

3 * 2 = 6
3 * 5 = 15

So, the expression becomes:

3 * (2 + 5) = 6 + 15 = 21

In summary, the distributive property allows us to simplify expressions by distributing a number to each term within parentheses. Remember to perform the multiplication individually and then combine the results using addition or subtraction.

More Answers: