Monomial

An algebraic expression that contains only one non-zero term is known as a monomial. A monomial is a type of polynomial, like, a binomial and trinomial, which is an algebraic expression having only a single term, which is a non-zero. It consists of only a single term which makes it easy to do the operation of addition, subtraction, and multiplication.

Examples:

• g is a monomial in one variable.
• 9cb² is a monomial in two variables c and b.
• 3a²b is monomial in two variables a and b.
• 4ab/5m is monomial in three variables a, b, m.
• -2m is a monomial in one variable m.

The different parts of a monomial expression are:

• Variable: The letters present in the monomial expression are variables.
• Coefficient: The number before a variable or the number multiplied by a variable in the expression.
• Literal Part: The alphabets which are present along with the exponent values are the literal part.

Monomial Examples – 6xy²

• Coefficient is 6
• Variables are x and y
• Degree of monomial expression = 1 + 2 = 3
• The literal part is xy²

Monomial Degree

The sum of exponent values of variables in the expression is called the degree of monomial or monomial Degree. If variables don’t have any exponent values its implicit value is 1.

Example:

4xy³, In this exponent value of x is 1. 

degree of expression is 3 + 1 = 4.

Monomial Operations 

The arithmetic operations which are performed on the monomial expression are addition, subtraction, multiplication, and division.

Addition of Two monomials:

When we add two monomials with the same literal part, it will result in a monomial expression. 

Example:

Addition of 2xy + 4xy = 6xy

Subtraction of Two monomials:

When we subtract two monomials with the same literal part, it will result in a monomial expression.

Subtraction of 6ab – 4ab = 2ab.

Multiplication of Two monomials:

When we multiply two monomials with the same literal part, it will result in a monomial expression.

Product of 2a²b * 6x = 12a²bx

Division of Two monomials:

When we divide two monomials with the same literal part, it will result in a monomial expression.

Division of x⁶ by x² = x⁴

Types of Polynomials: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. There are mainly four types of polynomials based on degree-constant polynomial (zero degree), linear polynomial ( 1st degree), quadratic polynomial (2nd degree), and cubic polynomial (3rd degree).

There are 3 types of polynomials based on the number of terms in the polynomial – monomial, binomial, and trinomial, and for more than that we use the general term polynomial. This article is about the types of polynomials – Monomials, Binomials, and Polynomials in detail.