Key takeaway: Like terms are terms that have exactly the same variable part, such as 6a and −2a, so they can be combined into one term by adding their coefficients.
Grade 66.EE.A.3Expressions and Equations
Definition of Like Terms
Like terms are terms whose variable parts match exactly, letter for letter and exponent for exponent. Only the coefficients are allowed to differ. The terms \(6a\) and \(-2a\) are alike; \(6a\) and \(6b\) are not, and neither are \(3x\) and \(3x^2\). Plain numbers also count as like terms with each other.
Because they name the same kind of object, you can add or subtract them, much like 6 apples minus 2 apples leaves 4 apples. Unlike terms cannot merge, just as apples and oranges stay separate in a fruit count. Spotting matching variable parts is the first move in simplifying almost every expression, so it pays to underline or color the matching groups before you add anything.
Formula and notation
Combining works on the coefficients and keeps the variable part:
\[6a – 2a = (6 – 2)a = 4a\]
The distributive property explains why: \(6a – 2a\) is \((6 – 2)a\). Terms with different variable parts cannot merge, so they are written side by side with their signs, like \(4a + 8b\).
Key facts
- The variable part must match completely, including every exponent.
- Constants are like terms with one another, so 9 and −4 combine to 5.
- The order of the terms does not matter, but each sign stays with its term.
- Collecting them first often makes an expression much shorter.
Like Terms example
Simplify \(6a + 9 – 2a + 5b – 4 + 3b\).
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Group the \(a\)-terms: \(6a – 2a = 4a\).
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Group the \(b\)-terms: \(5b + 3b = 8b\).
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Group the constants: \(9 – 4 = 5\).
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Write the results together: \(4a + 8b + 5\).
The simplified expression is \(4a + 8b + 5\).
Common mistake
Watch out
Hugo combines \(4a + 8b\) into \(12ab\).
Why it is wrong
The terms \(4a\) and \(8b\) have different variable parts, so they are not alike and cannot merge. Test it with \(a = 1\) and \(b = 1\): \(4 + 8 = 12\), but with \(a = 2\), \(b = 1\): \(8 + 8 = 16\), while \(12ab = 24\). Leave \(4a + 8b\) as it is.
Related terms and lessons
- Grade 6 · Writing and Evaluating Algebraic ExpressionsLessonWorksheetQuiz
- Grade 7 · Equivalent ExpressionsLessonWorksheetQuiz
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