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Monomial is a type of polynomial that consists of only one non-zero term. This single term can be a constant number, a variable, or a product of numbers and variables, where the variables have non-negative integer exponents. Monomials are the simplest forms of polynomials and are fundamental in algebraic expressions and equations. This article explores the concept of Monomial in detail and makes it easy to grasp for all the readers of the article without regard to their academic level. All subtopics, such as their monomial meaning, polynomial, monomial definition, monomial expression, example, and many many more, are covered in the article with plenty of examples. So, let’s start our journey to the land of monomials and understand this concept of Monomial. Table of Content What is Monomial?A monomial is a single-term polynomial, which is an algebraic expression consisting of one term. This term can be a number (a constant), a variable (like x), or a product of numbers and variables with non-negative integer exponents. In general, a monomial can be written in the form [Tex]a \cdot x_1^{k_1} \cdot x_2^{k_2} \cdots x_n^{k_n}[/Tex], where:
Monomial Definition
For instance, 2xy is a monomial with two variables (x and y) and one coefficient. Parts of MonomialsThe various parts of the monomial are covered in the below table with examples.
Example of Monomial“Mono” refers to one. When polynomials are classified on the basis of the number of terms, the polynomials with only a single term are called monomials. Some of the examples of monomials are: Constant Monomials
Monomials with a Single Variable
Monomials with Multiple Variable
Degree of Monomial
This can be well understood by the following example. The exponents of all the variables are added to determine a monomial’s degree. It is always an integer that is not zero. For instance, the monomial xyz3 has a degree of 5.
The result of adding all these exponents is 1 + 1 + 3 = 5. Example 1: Find the degree of monomial -3x3y3. Solution:
Example 2: Find the degree of the monomial 9xy3 Solution:
Identifying a MonomialLets apply the properties of a monomial in order to identify a monomial in the below examples:
Let’s consider an example for better understanding. Example: Identify if the following are monomial or not?
Solution:
Monomial, Binomial and TrinomialA monomial expression is one which has only one term. For example, 3xy is a monomial. A binary expression is one which has two terms. For example, 3x+4y, 4xy+6z is a binomial. Similar to this, a trinomial is an expression with three terms. For instance, a trinomial is 4x2 + 2y + 6z or 5x+7xy+9z . Lets look into the table below for more clarification between the three terms:
Examples of Monomial, Binomial and TrinomialMonomial has one term, binomial has two terms and Trinomial has three terms.
Monomial and PolynomialA polynomial is an algebraic expression that shows the sum of monomials. A monomial is an expression in which variables and constants may stand alone or be multiplied.
Factors of MonomialsWe usually factor coefficient and variables independently while factoring monomial. A monomial can be factored just as easily as a whole number. Example: Factorize the monomial, 20y4. In the given monomial, 20 is the coefficient and y4 is the variable. The prime factors of the coefficient, 20; are 2, 2 and 5. The variable y4 can be factored in as y × y × y × y. Therefore, the complete factorization of the monomial is 20y4 = 2 × 2 × 5 × y × y × y × y.  Read More about Factoring Polynomial. Operation on MonomialsOperations on monomials involve:
Let’s discuss these operations in detail as follows: Addition of MonomialsTo add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same. Example: Add 10xy2 and -9xy2. Solution:
Subtraction of MonomialsTo subtract two or more monomials that are like terms, subtract the coefficients; keep the variables and exponents on the variables the same. Example: Subtract 10xy2 and -9xy2 Solution:
Monomial MultiplicationTo multiply a monomial by a monomial we get a monomial. The coefficients of the monomials are multiplied together and then the variables are multiplied. Example: Find the product of two monomials 2x and 2y. Solution:
Monomial DivisionTo divide a monomial by a monomial, divide the coefficients and divide the variables with like bases by subtracting their exponents. To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. Example: Divide 4xy by 2x. Solution:
Read More, Solved Problems on MonomialsProblem 1: Choose the monomials from the following expressions: (a) x3 (b) 4 – x Solution:
Problem 2: Factorize the monomial expression: 8xy. Solution:
Problem 3: Is 10y/x a monomial expression? Justify your answer. Solution:
Problem 4: Find the degree of monomial 48 xy3. Solution:
Practice Problems on MonomialsProblem 1: Multiply the monomials: 4x3 and 2x2. Problem 2: Simplify the expression: 3a4b2 · 5a2b3. Problem 3: Divide the monomials: 8x5/4x2. Problem 4: Add the monomials: 2x3 + 3x3. Problem 5: Subtract the monomials: 7y4 – 2y4. Problem 6: Find the product of the monomials: -2x4 · -3x2. FAQs on MonomialsDefine Monomial in Math.
Is x3 a Monomial?
Is ABC a Monomial?
What is a Constant Monomial?
What is the Degree of a Monomial?
How to Identify a Monomial?
What are some examples of monomial?
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| Mathematics |
Type: | Geek |
Category: | Coding |
Sub Category: | Tutorial |
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