Key takeaway: A term in algebra is one part of an expression separated from the others by addition or subtraction, and it can be a number, a variable or a product of both.
Grade 66.EE.A.2bExpressions and Equations
Definition of Term
A term in algebra is a single piece of an expression. Terms are the parts joined by plus or minus signs. The expression \(4x^2 – 7x + 12 – 3y\) has four terms: \(4x^2\), \(-7x\), \(12\) and \(-3y\).
Each term can be a lone number, a lone variable, or a product of numbers and variables. Multiplication does not split a term: \(5xy\) is one term made of the factors 5, \(x\) and \(y\). The sign that comes before a term travels with it, so subtraction is read as adding a negative term. Knowing exactly what a term in algebra is makes later skills easier: you cannot combine, factor or simplify an expression until you can see where each term begins and ends. A good habit is to circle each term, with its sign, before doing anything else.
Formula and notation
Terms are the pieces between the signs. The names depend on how many there are:
\[3x \ (\text{one term}) \qquad 3x + 5 \ (\text{two terms}) \qquad 3x + 5 – 2y \ (\text{three terms})\]
Parentheses can hold several terms together, such as \(2(x + 3)\), which is one product but contains the sum \(x + 3\).
Key facts
- Plus and minus signs separate terms, while multiplication and division stay inside one term.
- A term includes the sign written in front of it.
- Any term in algebra without a variable is called a constant term.
- Terms with the same variable part can be combined into one.
Term example
How many terms does \(4x^2 – 7x + 12 – 3y\) have? List them, and say which one is a constant term.
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Mark the plus and minus signs that separate pieces: before \(7x\), before 12, before \(3y\).
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Those three signs divide the expression into four pieces: \(4x^2\), \(-7x\), \(12\), \(-3y\).
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Only 12 has no variable.
There are 4 terms, and the constant term is 12.
Common mistake
Watch out
Mateo says \(5xy\) has three terms because it contains 5, \(x\) and \(y\).
Why it is wrong
Those three are factors, not terms. Terms are separated by addition or subtraction, and \(5xy\) has none, so it is a single term. For example, \(5x + y\) has two terms.
Related terms and lessons
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