[Maths Class Notes] on Monomial in Maths Pdf for Exam

A monomial in Maths is a type of polynomial that has only one single term. For example, 4p + 5p + 9p is a monomial because when we add the like terms it will obtain the result as 19p. Furthermore, 4x, 21x²y, 9xy, etc are monomials because each of these expressions includes only one single term. As we know, polynomials are the algebraic expressions or equations which include variables and coefficients and have one or more than one term.Each term of the polynomial is a monomial. A polynomial includes the operations of addition, subtraction, multiplication and non-negative integer exponents of variables. In this article, we will study polynomial, monomial definition, monomial problems monomial examples, degree of monomial etc.

Polynomial

Polynomials are expressions that include exponents that are added, subtracted, multiplied, or divided. There are different types of polynomial such as monomial, binomial, trinomial, and zero polynomial. A monomial is a type of polynomial with one single term. A binomial is a polynomial with a maximum of two unlike terms. A trinomial is a polynomial with a maximum of three unlike terms.

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Monomial Definition

A monomial is a special kind of polynomial, which is an algebraic-expression having only one single term which is non-zero. It includes only one single term which simplifies the operation of addition, subtraction or multiplication. It includes only a single variable or coefficient or product of variable or coefficient with exponents as a whole number, which denotes only one single term unlike binomial or trinomial which includes two or three terms. Monomials in Maths do not have a variable in the denominator.

For example, 3x is a monomial, as it represents only one single term. Similarly, 23, 3x², 7xy, etc.are examples of monomials but 13 + x, 3xy, 4xy -1 are not considered as monomials because  they don’t satisfy conditions.

Monomial is a product of powers with non-negative integers. For example, if there is a one- variable p, then it will have a power either 1 or power of pⁿ with n as any positive integer and the product of the multiple variables such asPQR, then the monomial will be represented in the form of paqbrc.  Here a, b and are non-negative integers. Monomial in terms of the coefficient is defined as the term with a non-zero coefficient. 

Binomial

A binomial is an algebraic expression or a polynomial which has a maximum two, unlike terms. For example, 2x + 5x² is a binomial as it has two unlike terms that is 2x and 5x².

Trinomial

A trinomial is an algebraic expression or a polynomial that  has a maximum of, three unlike terms. For example, 2x + 5x² + 7x³ is a trinomial as it has three unlike terms that is 2x ,5x² and  7x³.

Finding the Degree of a Monomial

The degree of a monomial is the addition of the exponent of all the included variables which together forms a monomial. For example, pqr³ have 4 degrees 1,1,and 3. Therefore, the degree of pqr³ is 1 + 1 + 3 = 5.

Monomials Examples

• x – Here, the variable is one i.e x  and degree is also one.

• 6x² – Here, the coefficient is 6 and the degree is 2

• x³y – Here, x and y are two variables and the degree is 4(3+1).

• -6xy – Here, x and y are two variables and a coefficient is – 6.

Monomial Problem

1. Identify which one of the given below is a monomial.

1. 4xy

2. 4y + z

3. 3x² + 3y

4. x + y + z²

Solution: 4xy is a monomial whereas 4y + z , 3x² + 3y are binomials and x + y + z² is a trinomial.

Solved Examples –

1. (x³y) (x²y³) 

 Solution: (x³x²) (yy³)  

= x3 + 2 y1 + 3

= x5y4   

2. Solve the monomial expression 16q + 7q – 2q-(-4q)

Solution:  23q – 2q + 4q

= 21q + 4q

= 26q

3. (4x² + 3x -14 )+ (x³ – x² + 7x + 1)

Solution: (4x² + 3x -14 )+ (x³ – x² + 7x + 1)

Grouping the like terms, we get

x³ + (4x² – x²) + ( 3x+ 7x) + (-14 +1)

Simplifying the above expression we get,

= x³ + 3x² + 10x – 13

Quiz Time

1. In the expression -3x⁴, the coefficient is

1. x

2. 4

3. -3

2. Which of the following has a similar value as ( t t t t t t) (zzzz)

1. (t²z)⁴

2. (6t) (4z)

3. (t³z²)²