# When is it necessary to apply the distributive property?

## Question:

When is it necessary to apply the distributive property?

## The Distributive Property:

We have many different properties within the study of mathematics. The distributive property is one of these properties, and it states that if A, B, and C are mathematical expressions, then A(B + C) = AB + AC.

Anytime that we want to multiply a mathematical expression by a sum of mathematical expressions, it is necessary to use the distributive property. For example, suppose we wanted to multiply x by x2 + 3x + 1. To do this, we would need to apply the distributive property by multiplying x by each of the terms in x2 + 3x + 1, and adding up the products. This would go as follows:

• x(x2 + 3x + 1) = xx2 + x ⋅ 3x + x ⋅ 1 = x3 + 3x2 + x

This gives an example of applying the distributive property, and illustrates that anytime that we want to multiply a mathematical expression by a sum of mathematical expressions, then it is necessary to apply the distributive property. 