Topic: Introduction to Algebra

Subtopic: Basic Algebraic Processes

**Overview**

This lesson covers the basic processes of simplifying and evaluating algebraic expressions. The distributive law (a.k.a. distributive property), collecting like terms (a.k.a. combining like terms), and simplifying expressions are the main focus of this lesson. Learn them well! There is lots of new terminology to learn along with the algebraic processes. This material is needed to build a strong foundation of beginning algebra skills.

One caution to note is the difference between an "algebraic expression" and an "algebraic equation". The former may be able to be simplified but can never be solved. But an equation contains an equals sign and can therefore be solved (and the answer checked by substitution).

Another caution is that when you do check a solution in an equation (or evaluate an expression for a given value) be sure to substitute the value in using parentheses or you may make sign errors. E.g., evaluating x^{2} given that x=-3 would be (-3)^{2} and not -3^{2}. Note that (-3)^{2}=9 and -3^{2}=-9 so the parentheses make a huge difference!

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 1.1.1 Evaluate algebraic expressions
- 1.1.2 Check if a given value is actually a solution to an equation
- 1.1.3 Translate words into an algebraic expression or equation
- 1.1.4 Model real-life data with an algebraic equation
- 1.1.5 Recognize the properties of algebra: commutative, associative
- 1.1.6 Collect like terms
- 1.1.7 Use the distributive law (forward and backward)
- 1.1.8 Apply order of operations to simplify an expression
- 1.1.9 Factor an algebraic expression via the distributive law

**Terminology**

Terms you should be able to define: variable, constant, algebraic expression, term, coefficient, exponent, power, order of operations, "like" terms, equivalent expression, commutative property, associative property, equation, solution, equation vs. expression, distributive law, factor, factor vs. term

**Text Notes**

As you study definitions of the commutative and associative properties in your text, I suggest that you know how these rules work more than what their names are. For instance it is important to know that x*y = y*x but not as important that this is the "commutative law of multiplication" (IMO).

**Supplementary Resources**

Here are a couple of charts that help you translate from words to an algebraic expression or equation:

- Prof. Keely's Translating Words into Algebra Chart
- Words for Operations Reference Chart, Understanding Algebra by James Brannon

**Review Pre-Algebra:** Feeling like you need to spend a bit of time reviewing pre-algebra / arithmetic topics? I have links to lessons, videos, and some games covering the main topics from pre-algebra in my Just-In-Time Mathematics website (Note: This site is no longer maintained so some links may be broken.)