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Whenever you’re working with algebra, it’s really important that you know what a term is. The terms of an expression are separated by pluses and minuses:
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In this number sentence, 12 is a term, but so is
You’ll now see how things turn out when we invite variables to the party. The terms are separated in exactly the same way. Whenever you see a
A numerical expression consists of terms. Adding one term to another is called a sum, while subtracting one term from another is called a difference.
Formula
TERM
TERM
When you add or subtract terms containing variables, you can only do so with terms that are like. Terms are like when they have the same combination of variables, and the same degree, or exponent. The numbers in front of the terms—the coefficients—don’t have to be the same.
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Here
So far you’ve only seen expressions with like variables. But what happens if the terms have unlike variables? The method you should use is called collection.
Rule
In the examples below you will see that each term is marked with a color. Terms that are like will have the same color.
Example 1
Sort the terms in
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such that
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Example 2
Sort the terms in
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such that
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