Term (Algebra)
In short: A term in algebra is one part of an expression that is joined to the others by addition or subtraction, such as 5x, -2y or 9 in 5x – 2y + 9.
6th GradeAlgebra6.EE.A.2b
What is Term?
Every term in algebra is a building block. It may be a number alone, a variable alone, or a product and quotient of numbers and variables. Plus and minus signs act like fences between the blocks.
Precisely, the expression \(5x – 2y + 9\) has three terms: \(5x\), \(-2y\) and \(9\). Each term carries the sign in front of it. Parts multiplied together, like \(3 \cdot a \cdot b\), stay inside one term, and anything inside parentheses counts as part of one group.
How to spot it
- A question asks how many terms an expression has, or which term has a given variable.
- An expression is rewritten by moving or combining pieces separated by plus or minus.
- A polynomial is named by the count of its pieces, like binomial or trinomial.
- A list of parts includes a number with no letter, called a constant term.
The method
- Circle each plus or minus sign that is not inside parentheses.
- Cut the expression at those signs and keep each sign with the piece that follows it.
- Count the pieces; each one is a term in algebra, including a lone number.
- Name the type: a constant has no variable, and a variable term has a coefficient times a letter.
Term: solved example
Problem
How many terms are in \(7a^2 – 3ab + 12 – \frac{b}{4}\)? List them with their signs.
Solution
Cut at the signs: \(7a^2\), \(-3ab\), \(+12\) and \(-\frac{b}{4}\).
That makes 4 terms. The product \(3ab\) stays one term because only multiplication joins its factors.
Try it
Question 1
How many terms are in \(2(x + 5) – 9\)?
Show the answer
Two: \(2(x + 5)\) is one group and \(-9\) is the other.
Question 2
Name the constant term in \(x^2 – 6x + 14\).
Show the answer
The term with no variable is 14.
Term vs. Like Terms
A term is any single piece of an expression. Like terms are two or more pieces that have exactly the same variable part, such as \(4x\) and \(9x\), so they can be combined into one.
Keep going
Lessons
Worksheets and quizzes
- Writing and Reading Algebraic Expressions – Worksheet
- Writing and Reading Algebraic Expressions – Quiz
- Equivalent Expressions and the Distributive Property – Worksheet
- Equivalent Expressions and the Distributive Property – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Algebra