CLASS-6
TYPES OF ALGEBRAIC EXPRESSION
TYPES OF ALGEBRAIC EXPRESSION -
Algebraic expressions can be categorized into several types based on their structure and characteristics. Here are some common types of algebraic expressions:-
1. Monomial:- A monomial is a single algebraic term consisting of a constant and/or a single variable raised to a non-negative integer exponent.
For example-
- 3x²
- 4y
- 5
- 3x
- 2x²
Above all are monomials.
2. Binomial:- A binomial is an algebraic expression composed of exactly two unlike terms connected by addition or subtraction.
For example-
- 2x + 3
- 5y - 7
- x²- 4
- 2x + 3
- 5y - 2
Above all are binomials.
3. Trinomial:- A trinomial is an algebraic expression composed of exactly three unlike terms connected by addition or subtraction.
For example-
- 3x² + 2x + 1
- x² - 4x + 7
- 5x²+ 6x - 9
- y²+ 3y - 6
- 3z²- 8y + 5
Above all are trinomial.
4. Polynomial:- A polynomial is a sum of one or more monomials, where each monomial is referred to as a term. Polynomials can have any number of terms, including zero terms (constant polynomials).
For example-
- 3x³+ 2x² + 8x - 10
- 8x³- 6x²- 3x + 7
- 15y³+ 8y²+ 5y - 9
- 3x⁶ + 2x⁵ + 8x³- 10x²+ 15
Above all are polynomial.
5. Constant Expression:- A constant expression is an algebraic expression consisting of a single constant value with no variables.
For example-
"5" or "-3.14" are constant expressions.
6. Rational Expression:- A rational expression is an algebraic expression in the form of a fraction, where both the numerator and denominator are polynomials.
For example -
(3x² + 2x + 1)
- ------------------------
(2x + 3)
(8x³- 6x²- 3x + 7)
- -------------------------------
(x² - 4x + 7)
Above all are rational expression.
7. Radical Expression:- A radical expression contains one or more square roots, cube roots, or other types of roots.
For example-
- √(x² + 9)
- ∛(8y³- 27)
Above all are radical expressions.
8. Exponential Expression:- An exponential expression involves variables raised to exponents.
For example -
"2^x" or "3^(2y - 1)" are exponential expressions.
9. Algebraic Fraction:- An algebraic fraction is a fraction in which the numerator and denominator are both polynomials.
For example -
(5x²- 3x + 2)
- -------------------------
(2x + 3)
(2x³- 4x²- 5x + 10)
- ---------------------------------
(3x² + 2x + 5)
Above all are algebraic fraction.
10. Linear Expression:- A linear expression is a polynomial of degree 1, meaning it contains only terms with variables raised to the first power.
For example -
"3x + 2y - 5" is a linear expression.
11. Quadratic Expression:- A quadratic expression is a polynomial of degree 2, meaning it contains at least one term with a variable raised to the second power.
For example-
"ax²+ bx + c" is a quadratic expression.
These are some of the common types of algebraic expressions. Algebraic expressions are used to represent mathematical relationships, solve equations, and model real-world situations in various fields of mathematics and science. The classification of an algebraic expression into one of these types depends on its structure and the types of terms it contains.