Combining like terms without combining things that only look alike
Terms combine only when their variable parts match exactly. The coefficients change; the variable structure does not.
LaTeX article Updated July 13, 2026
A term has two jobs
The coefficient tells how many copies there are; the variable part tells what kind of object is being counted. Like terms have identical variable parts, including every exponent.
That is why 3x and 5x combine, but 3x and 5x² do not. They name different algebraic quantities.
Signs travel with their terms
A minus sign immediately before a term belongs to that term. When you rearrange an expression, move the sign with the coefficient.
Rewriting subtraction as addition of a negative makes this explicit and reduces dropped-sign errors.
Distribute before you collect
Parentheses may hide terms that are not ready to combine. Use the distributive property first, then group matching variable parts.
A negative multiplier must reach every term inside the parentheses, not just the first one.
Worked example
Common mistakes
- Adding exponents when adding terms.
- Combining x with x².
- Leaving a minus sign behind when rearranging.
Keep these ideas
- Variable parts must match exactly.
- Only coefficients combine.
- Distribute before collecting terms.