In view of the coronavirus pandemic, we are making LIVE CLASSES and VIDEO CLASSES completely FREE to prevent interruption in studies
Maths > Algebraic Expressions > Monomials, Binomials, Trinomials and Polynomials
Algebraic Expressions

Monomials, Binomials, Trinomials and Polynomials

Before we move to the terms of an algebraic expression, you need to recall the definition of an algebraic expression. As discussed in the previous topic, an algebraic expression is an amalgam of variables and constants of 1 or more terms. The expressions are separated by symbols or operations like (+, –, × and ÷). These expressions are categorized as a monomial, binomial, trinomial and polynomial. Let us know more!

Suggested Videos

Play
Play
Play
Arrow
Arrow
ArrowArrow
Square Identities
Types of Polynomials
Terms used in Algebraic Expressions
Slider

Related Question – 

A ball is drawn at random from box  and transferred to box . If the probability of drawing a red ball from box , after this transfer, is , then the correct option(s) with the possible values of  and  is (are). Check the answer here.

Introduction

Before we move any further, let us take help of an example for better understanding. Here are some examples of algebraic expressions.

  • 7b + 5m,
  • 5x + 3y + 10,
  • 5x/y + 3,
  • x + y + z,

Terms of An Algebraic Expression

Every part of an algebraic expression that is separated by a minus or plus sign is known as the term of the algebraic expression. Please note that multiplication and division sign does not separate the terms of an algebraic expression.

(Source: Pinterest.com)

Types of Algebraic Expressions

Broadly, there are five types of algebraic expressions. These include:

  • Monomial
  • Binomial
  • Trinomial
  • Polynomial
  • Multinomial

However, here in this topic, we’ll study about the first 4 categories of an algebraic expression.

Monomial

A monomial is an algebraic expression that has only one non zero term. Examples of a monomial expression:

  • a is a monomial in one variable a
  • 10ab2 is a monomial in two variables a and b.
  • 5m2n is a monomial in two variables m and n.
  • -7pq is a monomial in two variables p and q.
  • 5b3c is a monomial in two variables b and c.
  • 2b is a monomial in one variable b.
  • 2ax/3y is a monomial in three variables a, x and y.
  • k2 is a monomial in one variable k.

Binomial

A binomial is an algebraic expression that has two non-zero terms. Examples of a binomial expression:

  • a2 + 2b is a binomial in two variables a and b.
  • 5x3 – 9y2 is a binomial in two variables x and y.
  • -11p – q2 is a binomial in two variables p and q.
  • m + n is a binomial in two variables m and n.
  • b3/2 + c/3 is a binomial in two variables b and c.
  • 5m2n2 + 1/7 is a binomial in two variables m and n.

Trinomial

A trinomial is an algebraic expression that has three non-zero terms. Examples of a trinomial expression:

  • x + y + z is a trinomial in three variables x, y and z.
  • 2a2 + 5a + 7 is a trinomial in one variables a.
  • xy + x + 2y2 is a trinomial in two variables x and y.
  • -7m5 + n3 – 3m2n2 is a trinomial in two variables m and n.
  • 5abc – 7ab + 9ac is a trinomial in three variables a, b and c.
  • x2/3 + ay – 6bz is a trinomial in five variables a, b, x, y and z.

Polynomial

A polynomial is an algebraic expression that has one, two or more terms. Examples of polynomials:

  • 2a + 5b is a polynomial of two terms in two variables a and b.
  • 3xy + 5x + 1 is a polynomial of three terms in two variables x and y.
  • 3y4 + 2y3 + 7y2 – 9y + 3/5 is a polynomial of five terms in two variables x and y.
  • m + 5mn – 7m2n + nm2 + 9 is a polynomial of four terms in two variables m and n.
  • 3 + 7x5 + 4x2 is a polynomial of three terms in one variable x.
  • 3 + 5x2 – 4x2y + 5xy2 is a polynomial of three terms in two variables x and y.
  • x + 5yz – 7z + 11 is a polynomial of four terms in three variables x, y and z.
  • 1 + 2p + 3p2 + 4p3 + 5p4 + 6p5 + 7p6 is a polynomial of seven terms in one variable p.

Learn about Different types of Polynomials here.

Question For You

Question 1: Identify the Monomial, Binomial, Trinomial, Polynomial, and Multinomial from the following:

a) 5pq                      b) 3b + 5c

c) x + y + z             d) a2+ 2b

Answer : a) Monomial             b) Polynomial

c) Trinomial              d) Binomial

Question 2: Explain monomial with example?

Answer: A monomial refers to an expression that involves one term, like 3xy. Monomials include variables, numbers, and whole numbers whose multiplication takes place together. Any number, all by itself, can be a monomial, like the number 5 or the number 2,700.

Question 3: Explain the difference between polynomial and monomial?

Answer: A monomial refers to an expression that comprises of only one term. A polynomial, on the other hand, refers to an expression that has at least one algebraic term, but it does not give any indication of division by a variable or involves variables with fractional exponents.

Question 4: Explain the greatest monomial factor?

Answer: In order to find the greatest common factor (GCF) among monomials, one must take each monomial and write down its prime factorization. Afterwards, one must identify the factors that are common to each monomial. Then one must do multiplication of those common factors together.

Question 5: Is it possible for a degree of a monomial to be negative?

Answer: It is not possible for a degree of a monomial to be a negative value. A monomial is a single term that involves any combination of non-negative powers of variables and constants.

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

Browse

Algebraic Expressions

Leave a Reply

avatar
  Subscribe  
Notify of

Browse

Algebraic Expressions

Stuck with a

Question Mark?

Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps.
toppr Code

chance to win a

study tour
to ISRO

Download the App

Watch lectures, practise questions and take tests on the go.

Get Question Papers of Last 10 Years

Which class are you in?
No thanks.