Types of Algebraic Expressions
Algebraic expressions are classified by the number of terms they have. A term is a part of the expression separated by + or − signs.
Knowing the type helps in naming expressions and understanding their structure.
What is Types of Algebraic Expressions - Grade 7 Maths (Algebraic Expressions)?
Classification by number of terms:
- Monomial: An expression with 1 term. Examples: 5x, −3y², 7.
- Binomial: An expression with 2 terms. Examples: x + 3, 2a − b.
- Trinomial: An expression with 3 terms. Examples: x² + 3x + 2, a − b + c.
- Polynomial: An expression with one or more terms where variables have whole number exponents. Monomials, binomials, and trinomials are all polynomials.
Types of Algebraic Expressions Formula
Monomial: 1 term | Binomial: 2 terms | Trinomial: 3 terms
Types and Properties
Based on Degree:
- Linear expression: Highest power of variable = 1. Example: 3x + 2.
- Quadratic expression: Highest power = 2. Example: x² + 5x + 6.
- Cubic expression: Highest power = 3. Example: x³ − 2x.
Solved Examples
Example 1: Classifying Expressions
Problem: Classify: (a) 5x³ (b) 2a + 3 (c) x² − x + 1
Solution:
- (a) 5x³ → 1 term → Monomial
- (b) 2a + 3 → 2 terms → Binomial
- (c) x² − x + 1 → 3 terms → Trinomial
Example 2: Identifying Degree
Problem: Find the degree of 4x³ − 2x² + x − 7.
Solution:
- Highest power of x = 3
Answer: Degree = 3 (cubic expression).
Example 3: Is it a Polynomial?
Problem: Is 3/x + 2 a polynomial?
Solution:
- 3/x = 3x⁻¹, which has a negative exponent.
- Polynomials require whole number exponents.
Answer: No, it is not a polynomial.
Real-World Applications
Why classification matters:
- Different types have different factorisation methods.
- Monomials multiply simply; binomials and trinomials require distribution.
- Degree determines the number of solutions (roots) an equation can have.
Key Points to Remember
- Monomial: 1 term. Binomial: 2 terms. Trinomial: 3 terms.
- The degree is the highest power of the variable.
- Polynomials have whole number exponents only.
- Expressions with negative or fractional exponents are NOT polynomials.
Practice Problems
- Classify: 7ab
- Classify: 3x² − 5
- Classify: a + b + c − d
- Find the degree of 2x⁴ − 3x + 1.
- Is √x + 2 a polynomial?
Frequently Asked Questions
Q1. What is a monomial?
An algebraic expression with exactly one term. Examples: 5x, −3y², 7.
Q2. What is the degree of a polynomial?
The highest power of the variable in the expression. For 3x² + 2x − 1, the degree is 2.
Q3. Is a constant a polynomial?
Yes. A constant like 5 is a polynomial of degree 0.
