Lesson 1: Introducing algebraic expressions

Introduction

The topic Algebraic expressions is actually about changing the form of algebraic expressions. Most of the time, this involves writing an expression in a shorter, more concise way (simplifying). But not always. Sometimes an expression will be more useful to us in a different form, even if the new form does not look any shorter or more concise. Don't worry, this will start to make sense as you work your way through the course.

What's the difference between a TERM and an EXPRESSION?

A TERM is either a number, a letter or a combination of a number and letter(s) multiplied together (or divided).

Here are some examples of TERMS.

\(5~~~~~~~n~~~~~~~2t~~~~~~~12ab~~~~~~~3x^5y^2~~~~~~~\Large\frac{x}{4}~~~~~~~\frac{2ab}{7}~~~~~~~\frac{5n^2}{2m}~~~~~~~\frac{3x^2z}{y^3}\)

The following are NOT terms but they are EXPRESSIONS.

\(n+5~~~~~~~2t-12ab+5~~~~~~~3x^5y^2+n~~~~~~~\Large\frac{2ab}{7}\normalsize-2t\)

An EXPRESSION is a collection of terms separated by + and/or - signs.

In fact, we can use the word EXPRESSION for all of these examples but the word TERM only applies to the first set of examples.

Practise to master

Which of the following are TERMS and which are only EXPRESSIONS?

1) \(x^2-4x + 2\)

Expression (consisting of three terms)

2) \(16x^2\)

Term (or an expression consisting of one term!)

3) \(\Large\frac{3x}{7}-\Large\frac{1}{2x}\)

Expression (consisting of two terms)

Answer yes or no to the following.

4) Is a term also an expression?

Yes, we use the word expression very broadly.

5) Is an expression also a term?

No, only if the expression consists of a single term.

6) A term is either a number, a letter or a combination of a number and letter(s) added      together. True or false?

False, not added, multiplied (or divided).

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