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How Do You Simplify Expressions?

In order to understand algebra, it is important to learn how to simplify expressions! By simplifying expressions, we are able to change a complex expression into a more compact and simple form. Before we start, let’s look at the definition of an algebraic expression.

An algebraic expression is a mathematical phrase in which constants and variables are combined using operation symbols (+, -, x, ÷).

How Do You Simply Expressions?

This process involves collecting like terms, which means subtracting or adding terms that are the same in an expression.

When simplifying expressions, keep in mind these four important terms:

Basic Rules and Steps For Simplifying Any Algebraic Expression

  1. Remove parentheses and brackets by multiplying factors. Ex: For the expression 3(2x+3), multiple the 3 by the 2x and by the 3 to get 6x+9.
  2. Use the exponent rule to remove grouping if the terms contain exponents. Ex: (x^2)^2 becomes x^4.
  3. Combine like terms by adding or subtracting coefficients. Ex: 5x+7x-3 becomes 12x-3.
  4. Combine the constants. Ex: 5x-3+7x+9 becomes 12x+6.

Let’s simply an expression using all of these basic rules and steps!

6(3+x) + 5(3x+4) – (x^2)^2

First, look to see if you can clear any parentheses. In this expression, we can get rid of the first two sets of parentheses.

= 18 + 6x + 15x + 20 – (x^2)^2

Second, when you see a term with an exponent raised to a power, use the exponent rule and multiply the exponents. So, (x^2)^2 becomes x^4.

= 18 + 6x + 15x + 20 – x^4

Third, look for any like terms. 6x and 15x are like terms since they have the same variable and power (which is 1). Combining these terms, we will get 21x.

= 18 + 21x + 20 – x^4

Last, look for any constants that you can combine. We have the constants 18 and 20 here, which becomes 38 when combined.

= 38+21x – x^4

Our expression is now simplified! All you have to do now is write the expression in the right order. Usually, you start with the term with the largest exponents and work your way down to the constants. So, our final expression is…

= x^4 + 21x +38

That is all for simplifying algebraic expressions! Just remember the four basic rules and steps, and you’ll be on your way to mastering algebra!

Sydney Le
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