# 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*.

## Answer and Explanation:

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 *x*2 + 3*x* + 1. To do this, we would need to apply the distributive property by multiplying *x* by each of the terms in *x*2 + 3*x* + 1, and adding up the products. This would go as follows:

*x*(*x*2 + 3*x*+ 1) =*x*⋅*x*2 +*x*⋅ 3*x*+*x*⋅ 1 =*x*3 + 3*x*2 +*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.

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from High School Algebra II: Help and Review

Chapter 2 / Lesson 20