MONOMIAL

Monomial

Definition Of Monomial

A Monomial is an algebraic expression containing only one term. For Example: 3xy²

More About Monomial

A monomial can be a constant number or a variable expression.
A monomial should not have negative and fractional exponents.
Example: a- 2 and a^1/2(are not monomials.)
A monomial multiplied by a monomial is also a monomial.
A monomial multiplied by a constant is also a monomial.

Video Examples: Monomials

Examples of Monomial

5, xy, 36x²y, a, 14b are the examples of monomial.
8x - 1, 2x² + 3x + 6 are not monomials.

Solved Example on Monomial

Ques: Which of the following expressions is a monomial?

Choices:

A. 9xy
B. 3x² + 7x + 2
C. 7x + 3
D. y- 2
Correct Answer: A

Solution:

Step 1: A monomial is an algebraic expression with only one term.
Step 2: Here, 3x² + 7x + 2 is not a monomial as there are three terms in the expression. [3x², 7x, and 3 are the three terms.]
Step 3: 7x + 3 is not a monomial as there are two terms in the expression. [7x and 3 are the two terms.]
Step 4: y- 2 is not a monomial as it is having a negative exponent.
Step 5: But, 9xy is a monomial as it is having only one term in the expression. [9xy is the only one term.]

Quick Summary

A monomial consists of only one term.
It can be a constant, a variable, or a product of both.
Exponents must be non-negative integers.

\[ ax^n \]

🍎 Teacher Insights

Use visual aids and concrete examples to help students differentiate between monomials and other algebraic expressions. Emphasize the importance of non-negative integer exponents.

🎓 Prerequisites

Basic Algebra
Understanding of Variables
Exponents

Check Your Knowledge

Q1: Which of the following is a monomial?

3x + 2 5y x^2 + x + 1 z - 3

Q2: Which of the following is NOT a monomial?

7 ab 4x^3 p + q

Frequently Asked Questions

Q: Is 5 a monomial?
A: Yes, 5 is a monomial because it is a constant term.

Q: Is x + y a monomial?
A: No, x + y is not a monomial because it has two terms.

Q: Is x^(-1) a monomial?
A: No, x^(-1) is not a monomial because it has a negative exponent.