Engineering Principles V11

Clive W. Humphris

ALGEBRA 1: Combining of Like Terms.  

Many students fear any mention of algebra and yet those same students can write complex computer programs with ease. Algebra and computer programming are pretty much the same. Both use variables and constants and symbols for addition, subtraction, multiplication and division. For each you are required to construct expressions by combining these symbols and variables and both conform to a set of rules or errors occur. For speed of computer processing each should be reduced to its simplest form.

Algebra enables us to manipulate variables, formulae and simplify expressions without have to concern ourselves with the actual values.

In this example we have a string of algebraic 'terms' i.e. 2a or -3a. Each of these terms has a fixed value (constant) and a letter 'a' for the variable. Terms written in this way are called products as they are a shorthand form of 2 × a, and -3 × a. See the algebra rules topic.

Combining the terms is fundamental to the simplification of an algebraic expression. Shown here as a series of additions, but could equally be subtractions. To solve just regroup the variables so it's easy to add (or subtract) all the positive terms and all the negative terms separately. Then sum the totals of the two groups. Finally calculate the result for your chosen value for a.

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