CLASS-6
ALGEBRA - MONOMIAL

MONOMIAL -

In algebra, a monomial is a specific type of algebraic expression that consists of a single term. A term in a monomial can be a constant, a variable, or the product of constants and variables raised to non-negative integer exponents. Here are some key characteristics and examples of monomials:

  1. Single Term:- A monomial contains only one term, which can be a combination of constants, variables, and exponents.
  2. Constants:- Constants in monomials are fixed numerical values that do not contain variables. They can be positive, negative, or zero.  For example, in the monomial "5," 5 is a constant.
  3. Variables:- Monomials can contain variables, which are symbols (usually represented by letters) that represent unknown or varying quantities. Variables can be raised to non-negative integer exponents. For example, in the monomial "3x²," "x" is the variable raised to the second power.
  4. Coefficients:- Coefficients are the numerical factors that multiply the variables and their exponents in a monomial. Coefficients can also be constants. For example, in the monomial "2y," the coefficient is 2.


Examples of Monomials:-

  1. Constant Monomial:- "7" is a monomial consisting of a constant. It's a simple monomial with no variables.
  2. Linear Monomial:- "4x" is a monomial consisting of the variable "x" raised to the first power and a coefficient of 4.
  3. Quadratic Monomial:- "10y²" is a monomial consisting of the variable "y" raised to the second power and a coefficient of 3.
  4. Constant Times Variable:- "2a" is a monomial consisting of a constant (2) and a variable "a."
  5. Variable Raised to Zero:- "1" is a monomial that may seem like just a constant, but it can also be considered a variable (any variable raised to the power of 0 is equal to 1).

Examples of Monomial (Another way of Understanding) -

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.

·     10ab²is 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.

·      k³ is a monomial in one variable k.

Monomials are the simplest form of algebraic expressions, and they can be added, subtracted, multiplied, and divided to form more complex algebraic expressions, known as polynomials. Understanding monomials is fundamental in algebra, as they are building blocks for more advanced mathematical concepts and equations.