Monomial vs Binomial vs Trinomial: Key Differences with Examples
The concept of Monomial in Maths plays a key role in algebra and is widely applicable in both real-life and exam situations. Learning about monomials helps build a strong foundation for more advanced maths topics, making problem-solving easier and more efficient.
What Is Monomial in Maths?
A monomial in maths is an algebraic expression that contains only one non-zero term. It can be only a number (constant), a variable, or the product of a constant and one or more variables, where the exponents of all variables must be non-negative integers. You’ll find this concept applied in areas such as algebraic expressions, polynomials, and simplifying equations.
Key Formula for Monomial in Maths
Here’s the standard form of a monomial: \( a \cdot x^m \cdot y^n \ldots \), where a is a real number (coefficient), variables have whole number (non-negative integer) exponents, and there’s just one term.
Monomial in Maths – Definition & Examples
A monomial in maths is an expression with a single term, made up of a number, a variable, or both multiplied together. No addition or subtraction signs appear within a monomial. For example:
- 5x
- 7
- -3xy²
- 4a³
- 2mnp
How to Identify a Monomial: Rules & Quick Tips
- It should have only one non-zero term.
- All variable exponents must be non-negative integers (e.g., x², not x−2 or x½).
- No variables should be present in the denominator.
- No addition or subtraction within the term.
Tip: A solitary number or a single variable is also a monomial (like 9 or y).
Monomial vs Binomial vs Trinomial
| Type | Definition | Example |
|---|---|---|
| Monomial | One term | 7x² |
| Binomial | Two terms (separated by + or -) | x + 5y |
| Trinomial | Three terms | 4x² + 2y + 6z |
Step-by-Step Illustration: Example Problem
Let's check if 8xy² is a monomial and find its degree:
1. Check for a single term.2. Confirm exponents: x (power 1), y (power 2) → all are non-negative integers.
3. No addition, subtraction, or variable in denominator.
4. It is a monomial.
5. Degree = 1 (x) + 2 (y) = 3.
Final Answer: 8xy² is a monomial of degree 3.
Try These Yourself
- Write any 5 examples of monomials.
- Find the degree of the monomial 3a4b2.
- Is 2x-1 a monomial?
- Identify the coefficient, variables, and degree in 6xy3.
Frequent Errors and Misunderstandings
- Thinking an expression with division by a variable (like 5/x) is a monomial—it is not.
- Mistaking negative exponents or fractional exponents as monomials.
- Assuming that having more than one variable automatically makes it a binomial (it still counts as one term if there's no + or -).
Degree of a Monomial: Simple Steps
The degree of a monomial is the sum of the powers of all its variables. If there’s no variable, degree is 0.
Example: In 4x²y³, degree = 2 + 3 = 5.
Tip: Look for the sum of exponents ONLY, don’t include the coefficient.
Monomial Operations (Addition, Multiplication)
You can add monomials with the same variables and exponents. To multiply monomials, multiply coefficients and add the exponents of matching variables.
Multiplication Example: Multiply 3xy × 5x².
1. Multiply coefficients: 3 × 5 = 152. Multiply variables: x × x² = x1+2 = x³; y remains y.
3. Final answer: 15x³y.
Relation to Other Concepts
The idea of monomial in maths connects closely with Algebraic Expressions and Polynomials. Knowing how to identify and work with monomials helps with solving equations, factorizing, and understanding topics like the degree of a polynomial.
Cross-Disciplinary Usage
Monomials in maths help in Physics for writing and simplifying formulas involving powers of variables, in Computer Science for polynomial time complexity, and in day-to-day tasks involving simple repeated multiplication. This is useful in exams like CBSE, JEE, and Olympiads.
Classroom Tip
A quick mnemonic: “Mono” means one—so a monomial always has just one term. In Vedantu’s live sessions, teachers often say, “If you only see multiplication (and no plus or minus in-between), you’re probably looking at a monomial!”
Wrapping It All Up
We explored monomial in maths from its definition, formula, classic examples, and common mistakes, to its links with expressions and polynomials. For more concept clarity on monomials, continue practicing on Vedantu and try related topics below to supercharge your exam scores.
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FAQs on Monomial in Maths: Meaning, Examples & How to Identify
1. What is a monomial in maths?
A monomial in maths is a single algebraic term. It can be a constant (like 5 or -2), a variable (like x or y), or a product of constants and variables with non-negative integer exponents (like 3x², -7xy, or 12). It contains no addition or subtraction signs.
2. Give 5 examples of monomials.
Here are five examples of monomials:
- 7 (a constant monomial)
- x (a variable monomial)
- -2y² (a monomial with a negative coefficient and a variable raised to a power)
- 4ab (a monomial with multiple variables)
- 1/2 x³y (a monomial with a fractional coefficient)
3. Is 3x² a monomial?
Yes, 3x² is a monomial. It has one term, a coefficient (3), a variable (x), and a non-negative integer exponent (2).
4. What is the difference between a monomial and a binomial?
A monomial has only one term, while a binomial has two terms separated by a plus or minus sign. For example, 5x is a monomial, and 5x + 2 is a binomial.
5. How do you find the degree of a monomial?
The degree of a monomial is the sum of the exponents of all its variables. For example, the degree of 5x²y is 3 (2 + 1 = 3). The degree of a constant monomial (like 7) is 0.
6. Can a monomial have a negative exponent?
No, a monomial cannot have a negative exponent. The exponents of the variables in a monomial must be non-negative integers (0, 1, 2, 3, and so on).
7. What is a constant monomial?
A constant monomial is a monomial that consists of only a number; it contains no variables. Examples include 5, -2, and 0.
8. How do you add two monomials?
You can only add monomials that are like terms (terms with the same variables raised to the same powers). Add the coefficients of like terms and keep the variables the same. For example: 3x² + 5x² = 8x²
9. How do you multiply two monomials?
To multiply two monomials, multiply their coefficients together and then multiply their variable parts together. Remember to add the exponents of like variables. For example: (2x)(3x²) = 6x³
10. What are like terms in monomials?
Like terms in monomials are terms that have the exact same variables raised to the exact same powers. For example, 3x²y and 5x²y are like terms, but 3x²y and 3xy² are not.
11. Is 5/x a monomial?
No, 5/x is not a monomial because it has a variable in the denominator. Monomials only have non-negative integer exponents.
12. What is the degree of 7x³y⁴z?
The degree of the monomial 7x³y⁴z is 8 (3 + 4 + 1 = 8). We sum the exponents of all the variables.
