Simplifying Algebraic Expressions

Introduction

In this lesson, we will learn how to simplify an algebraic expression. Before we start though, let's review the key term:

Key Term

• Expression uses variables, numbers, and operations to express values in Algebra

Simplifying Algebraic Expressions

Let's say that we have the following expression:

15 ( 2n + 3 ) - 10

In order to simplify this expression, we can use the Distributive Property.

Step 1:
Distribute 15 to 2n and 3.

15 x 2n = 30n
15 x 3 = 45

That means we now have
 30n + 45 -10

Step 2:
Combine Like Terms
Remember that Like Terms are terms that are alike and you can put together
Also remember that you can only combine variables with variables and constants with constants.

Variable: a letter used to replace a value in algebra
Constants: Numbers without a variable in algebra

So, our like terms are +45 and -10.

Think of it like this:
I have 45 dollars (+45) and I owe 10 dollars to a friend (-10). How many dollars do I have left?

To find the difference, we'll simply subtract!

45 - 10 = 35

That means we have 35 dollars left or +35!

Step 3:
Rewrite simplified expression!

15 ( 2n + 3 ) - 10

30n +45 - 10

30n +35