Math Doubts

Monomials

An algebraic expression that contains only one term is called a monomial.

Introduction

The meaning of monomial is defined from a prefix “Mono” and a Latin term “Nomial”.

  1. The meaning of Prefix “Mono” is one or single.
  2. The meaning of “Nomial” is a term.

By combining the meanings of both the terms, monomial is defined in algebra as an algebraic expression with one term. In algebra, a monomial is used to represent a quantity in algebraic form. It is known as a polynomial of one term. The monomials are expressed mathematically in two different algebraic forms.

Algebraic terms

Every algebraic term is an algebraic expression in a single term. So, each algebraic term is a monomial mathematically.

Examples

$(1) \,\,\,\,\,\,$ $a$

$(2) \,\,\,\,\,\,$ $-6b$

$(3) \,\,\,\,\,\,$ $3x^2y$

$(4) \,\,\,\,\,\,$ $\dfrac{2}{9} \, mn$

$(5) \,\,\,\,\,\,$ $-\dfrac{4pq^2}{r}$

Numbers

Every number is considered as a monomial.

Examples

$-2$$,\,$ $5$$,\,$ $\sqrt{7}$$,\,$ $\dfrac{4}{9}$$,\,$ $0.12 \,$ $\cdots$

There are two reasons for considering numbers as monomials.

  1. In Arithmetic, the quantities are symbolically represented by numbers and they are represented in the form of literals in algebra. So, they both are same in mathematics.
  2. Every number can be written in algebraic form. For example, the number $5$ can be written as an algebraic term $5x^0$.