Introduction to Evaluating, Simplifying, and Translating Algebraic Expressions

A U.S 1040 individual tax return form with a pencil lying on top of it


Have you ever had to fill out a tax form when starting a new job or filing your tax return at the end of the year? It can be a puzzling task, with lots of instructions such as “enter the sum of line 20 and line 32 into line 33” or “enter the difference between line 8 and line 9 into line 10.” The form might be telling you to do simple addition or subtraction, but it’s not always obvious due to the wording used. In this section, you’ll learn how to untangle algebraic expressions by identifying and combining like terms and translating words and phrases into familiar operations.


Learning Outcomes

By the end of this section, you will be able to:

  • Evaluate algebraic expressions
  • Identify terms, coefficients, and like terms
  • Simplify expressions by combining like terms
  • Translate word phrases to algebraic expressions


Before you get started in this module, try a few practice problems and review prior concepts.

readiness quiz


If you missed this problem, review this example:

Determine if each is an expression or an equation:

  1. [latex]16 - 6=10[/latex]
  2. [latex]4\cdot 2+1[/latex]
  3. [latex]x\div 25[/latex]
  4. [latex]y+8=40[/latex]


If you missed this problem, review this example:

Simplify: [latex]{3}^{4}[/latex].


If you missed this problem, review the video below.