Term

Term

Parts of an expression or series separated by + or – signs, or the parts of a sequence separated by commas.

Expression	Terms
5a³ – 2xy + 3	5a³, 2xy, and 3
	p, 2q, a², and b

See also

Polynomial

Key Formula

a_1,\; a_2,\; a_3,\; \ldots,\; a_n

Where:

$a_n$ = The nth term of a sequence or series
$n$ = The position number (index) of the term, starting from 1

Worked Example

Problem: Identify each term in the expression 4x² − 7x + 9 and state how many terms there are.

Step 1: Look for the addition and subtraction signs that separate the expression into parts.

4x^2 \;{\color{red}-}\; 7x \;{\color{red}+}\; 9

Step 2: The first term is everything before the first − sign.

\text{1st term: } 4x^2

Step 3: The second term is everything between the − sign and the + sign. Include the sign as part of the term's coefficient.

\text{2nd term: } -7x

Step 4: The third term is everything after the + sign.

\text{3rd term: } 9

Answer: The expression has three terms: 4x², −7x, and 9. It is called a trinomial because it contains exactly three terms.

Another Example

This example shows 'term' in the context of a sequence, where each term has a position number, rather than identifying terms within an algebraic expression.

Problem: Find the 6th term of the arithmetic sequence 3, 8, 13, 18, …

Step 1: Identify the first term and the common difference between consecutive terms.

a_1 = 3, \quad d = 8 - 3 = 5

Step 2: Use the formula for the nth term of an arithmetic sequence.

a_n = a_1 + (n - 1)d

Step 3: Substitute n = 6, a₁ = 3, and d = 5 into the formula.

a_6 = 3 + (6 - 1)(5) = 3 + 25 = 28

Answer: The 6th term of the sequence is 28.

Frequently Asked Questions

What is the difference between a term and a factor?

Terms are separated by addition or subtraction signs, while factors are quantities that are multiplied together within a single term. For example, in the expression 3xy + 5, the two terms are 3xy and 5. Within the first term, 3, x, and y are all factors because they are multiplied together.

Is a negative sign part of a term?

Yes. When a subtraction sign appears before a term, it is treated as a negative coefficient belonging to that term. In 6a − 2b, the second term is −2b (not just 2b). Carrying the sign with the term ensures you handle operations correctly.

What are like terms?

Like terms are terms that have the same variable parts raised to the same powers. For instance, 5x² and −3x² are like terms because both contain x². You can combine like terms by adding or subtracting their coefficients: 5x² + (−3x²) = 2x². Constants such as 7 and −4 are also like terms.

Term vs. Factor

	Term	Factor
Definition	A part of an expression separated by + or − signs	A quantity multiplied with other quantities inside a term
Operation that separates them	Addition or subtraction	Multiplication
Example in 3xy + 5	3xy and 5 are the two terms	3, x, and y are factors of the first term
Can be combined	Only like terms can be combined	Factors are simplified by canceling or multiplying

Why It Matters

Identifying terms is the first step in simplifying expressions—you must find like terms before you can combine them. In sequences and series, the concept of a term (and its position number) is essential for writing formulas and calculating sums. Nearly every algebra topic, from factoring polynomials to solving equations, requires you to correctly recognize and manipulate individual terms.

Common Mistakes

Mistake: Forgetting to include the subtraction sign with the term that follows it.

Correction: Always attach the sign directly in front of a term to its coefficient. In 10 − 3y, the second term is −3y, not 3y. Dropping the negative sign changes the value entirely.

Mistake: Confusing terms with factors, especially in products like 2(x + 3).

Correction: In 2(x + 3), the entire product is one term because nothing is added or subtracted outside the parentheses. Inside the parentheses, x and 3 are separate terms of the binomial (x + 3), while 2 and (x + 3) are factors of the whole expression.

Related Terms

Expression — A combination of terms, operations, and grouping symbols
Series — The sum of the terms of a sequence
Sequence — An ordered list of terms following a pattern
Polynomial — An expression whose terms have whole-number exponents
Coefficient — The numerical factor of a term
Like Terms — Terms with identical variable parts that can be combined
Constant — A term with no variable, just a number
Factor — Quantities multiplied together within a single term