Term

Intuition and core definition

A term is a single number, variable, or product of numbers and variables separated from other terms by top-level addition or subtraction. In $4x^2-3xy+7$, the terms are $4x^2$, $-3xy$, and $7$. The sign immediately before a term belongs to that term.

Notation, language, and conditions

A term may contain factors joined by multiplication and powers. Parentheses can keep a sum inside one factor: in $5(x+2)$, the expression has one product before expansion, while $5x+10$ has two terms. Like terms have identical variable parts with identical exponents, so only their coefficients differ.

Why this idea matters

A term is a signed additive component, so identifying term boundaries prevents illegal cancellation or combination across plus and minus signs.

A dependable method

1. Look only at addition and subtraction signs not enclosed in grouping symbols.
2. Split the expression at those top-level signs.
3. Attach each subtraction sign as a negative sign on the following term.
4. For each term, identify coefficient and variable part.
5. Group like terms only when their complete variable parts match.

Worked example

Common mistakes