Algebraic terms

A term that contains at least a literal number to represent a quantity is called an algebraic term.

Introduction

An algebraic term is a term that contains at least one literal. Algebraic terms are usually formed by the involvement of both numbers and literals in different possible combinations to represent quantities mathematically.

Formation

The algebraic terms are formed in four different ways possibly to represent quantities mathematically.

01 Numbers

Every number is a symbol and used to represent a particular quantity. Hence, every real number is a basic example to algebraic terms.

Examples

$0$, $3$, $-8$, $\dfrac{4}{7}$, $-\dfrac{13}{6}$, $0.56$, $-3.15$, $\sqrt{13}$, $-\dfrac{2}{\sqrt[\displaystyle 3]{9}}$, $\ldots$

02 Literals

Every symbol can be used to represent a quantity. Therefore, the symbols (can be either constants or variables) are also best examples of algebraic terms.

Examples

$a$, $p$, $\theta$, $\delta$, $c_o$, $\pi$, $\ldots$

03 Product form

Numbers and symbols involve in multiplication to form single terms as their product to represent quantities. So, every algebraic term can be formed in product form by a number and at least one symbol.

Examples

$2x$, $-p^{\displaystyle 2}$, $7ab$, $-6m^{\displaystyle 2}n$, $0.5rs^{\displaystyle 2}t^{\displaystyle 3}$, $\Bigg(\dfrac{3}{7}\Bigg)cd^{\displaystyle 2}e^{\displaystyle 3}f^{\displaystyle 4}$, $\ldots$

04 Quotient form

Numbers and symbols are also involved in division to form single terms as their quotient. Therefore, every algebraic term can be formed in quotient form by a number and at least one symbol.

Examples

$\dfrac{1}{d}$, $-\dfrac{a}{2b}$ , $\dfrac{p^{\displaystyle 2}}{q}$, $-\dfrac{m^{\displaystyle 4}}{n^{\displaystyle 3}r^{\displaystyle 6}}$, $\ldots$