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Addition and Subtraction of Algebraic
Expressions

Terms and Factors
A term in an algebraic expression is an expression involving letters and/or
numbers (called factors), multiplied together
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It has factors 5 and x
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Example 2

5x + 3y has two terms
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Example 3

The expression
3𝑥 2 − 7𝑎𝑏 + 2𝑒√𝜋
has three terms
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Like Terms
"Like terms" are terms that contain the same variables raised to the same
power
Example 4

3𝑥 2 and 7𝑥 2 are like terms
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Adding and Subtracting Terms
Important: We can only add or subtract like terms
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On a table we have 4 pencils and 2 books
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We go get another 3 pencils and 6 books
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We can't combine these quantities, since they are different types
of objects
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We are left with 2 pencils and
we still have the 8 books
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Example 6

Simplify 13x + 7y − 2x + 6a

13x + 7y − 2x + 6a
The only like terms in this expression are 13x and 2x
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So we group together the terms we can subtract, and just leave the rest:

(13x − 2x) + 6a + 7y
= 6a + 11x + 7y
We usually present our variables in alphabetical order, but it is not essential
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We could
have used curly brackets { } here as well
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−2(m − 3n) = −2m + 6n
The negative times negative in the middle gives positive 6n
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So here's the answer:

−5[−2(m − 3n) + 4n] = 10m − 50n
Note:
The fancy name for round brackets ( ) is "parentheses"
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The fancy name for curly brackets { } is "braces"

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