Term

Algebra Term

A term is a mathematical expression or component consisting of constants, variables, and their product or quotient.

Terms are the basic building blocks of algebraic expressions and polynomials. They are separated by addition or subtraction signs within an expression.

The general form of a term is $ax^n$ , where $a$ is the coefficient (a constant), $x$ is the variable, and $n$ is a non-negative integer representing the exponent of the variable.

Basic Unit

A term is the most basic unit in an algebraic expression.

Contains Constants and/or Variables

A term can consist of numerical constants, variables, or their product or quotient.

Separated by Addition or Subtraction

In algebraic expressions, terms are combined using addition or subtraction.

Examples of Terms

Constant Term:
- $7$ : This is a constant term because it consists of a numerical constant with no variable.
Linear Term:
- $2x$ : This is a linear term because it consists of the product of a constant ( $2$ ) and a variable ( $x$ ).
Quadratic Term:
- $\text{-}3y^2$ : This is a quadratic term because it consists of the product of a constant ( $\text{-}3$ ) and a variable ( $y$ ) raised to the exponent $2$ .
Mixed Term:
- $4xy^2$ : This term is a mix of variables ( $x$ and $y$ ) and constants ( $4$ ).
Fractional Term:
- $\frac{1}{2}$ : This term is a fraction, and it represents the product of the constant $\frac{1}{2}$ and the variable $x$ .
Constant Times Variable with Exponent:
- $5a^3$ : This term involves a constant ( $5$ ) multiplied by a variable ( $a$ ) raised to the exponent $3$ .

Not Terms

Expressions with Variables in the Denominator:
- $\frac{2}{x}$ : This is not a single term because it involves a variable in the denominator.
Expressions with Variables in the Exponent:
- $3^x$ : This is not a term because the variable $x$ is in the exponent.
Sum or Difference of Terms:
- $2x+3$ : This is not a single term but an expression with two terms.