Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
What is an Algebraic Expression?
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
Examples
3x + 4y – 7, 4x – 10, etc.
These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression. It is to be noted that, unlike the algebraic equation, an algebraic expression has no sides or equal to sign. Some of its examples include
- 3x + 2y – 5
- x – 20
- 2x2 − 3xy + 5
Variables, Coefficient & Constant in Algebraic Expressions
In Algebra we work with Variable, Symbols or Letters whose value is unknown to us.
In the above expression (i.e. 5x – 3),
- x is a variable, whose value is unknown to us which can take any value.
- 5 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.
- 3 is the constant value term that has a definite value.
The whole expression is known to be the Binomial term, as it has two unlikely terms.
Types of Algebraic expression
There are 3 main types of algebraic expressions which include:
- Monomial Expression
- Binomial Expression
- Polynomial Expression
Monomial Expression
An algebraic expression which is having only one term is known as a monomial.
Examples of monomial expressions include 3x4, 3xy, 3x, 8y, etc.
Binomial Expression
A binomial expression is an algebraic expression which is having two terms, which are unlike.
Examples of binomial include 5xy + 8, xyz + x3, etc.
Polynomial Expression
In general, an expression with more than one term with non-negative integral exponents of a variable is known as a polynomial.
Examples of polynomial expression include ax + by + ca, x3 + 2x + 3, etc.
Other Types of Expression
Apart from monomial, binomial and polynomial types of expressions, an algebraic expression can also be classified into two additional types which are:
- Numeric Expression
- Variable Expression
Numeric Expression
A numeric expression consists of numbers and operations, but never include any variable. Some of the examples of numeric expressions are 10 + 5, 15 ÷ 2, etc.
Variable Expression
A variable expression is an expression that contains variables along with numbers and operation to define an expression. A few examples of a variable expression include 4x + y, 5ab + 33, etc.
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