Algebraic Expression Definition: An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations (addition, subtraction, etc.) Expressions are made up of terms.
3x+4y 7, 4x – 10 etc.
It is to be noted that, unlike algebraic equation, an algebraic expression has no sides or equal to sign. Some of its examples include
In Algebra we work with Variable, Symbols or Letters whose value is unknown to us.
In the above expression (i.e. 5x – 3),
The whole expression is known to be the Binomial term, as it has two unlikely terms.
There are 3 mains types of algebraic expressions which include:
An algebraic expression which is having only one term is known as a monomial.
Examples of monomial expression include 3x^{4}, 3xy, etc.
A binomial expression is an algebraic expression which is having two unlikely terms.
Examples of binomial include 5xy + 8, xyz + x^{3}, etc.
In general, an expression with more than one terms with nonnegative integral exponents of a variable is known as a polynomial.
Examples of polynomial expression include ab + bc + ca, etc.
Apart from monomial, binomial and polynomial types of expressions, alebraic expression can also be classsified into two additional types which are:
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.
A variable expression is an expression which contains variables along with numbers and operation to define an expression. A few examples of a variable expression include 4x+y, 5ab + 33, etc.
Example: Simplify the given expressions by combining the like terms and write the type of Algebraic expression.
(i) 3xy^{3} + 9x^{2} y^{3} + 8x^{3} + 5y^{3}x (ii) 7ab^{2} c^{2} + 2a^{3} b^{2} − 3abc – 5ab^{2} c^{2} – 2b^{2} a^{3} + 2ab (iii) 50x^{3} – 20x + 83 + 21x^{3} – 3x + 3 + 15x – 41x^{3} Solution: . Creating a table to find the solution:

An algebraic expression is a combination of constant, variables and algebraic operations(+, , ×, ÷). We can derive the algebraic expression for a given situation or condition by using these combinations.
For example, Sima age is thrice more than Tina. And the total age of Sima and Tina is 40. Expressing the algebraic form of this condition;
3x + x = 40 ⇒ 4x = 40; where x is the age of Tina.
No, not all algebraic expressions are polynomials. But all polynomials are algebraic expressions. The difference is polynomials include only variables and coefficients with mathematical operations(+, , ×) but algebraic expressions include irrational numbers as well.
Also, polynomials are continuous function(eg: x^{2} + 2x + 1) but algebraic expression may not be continuous sometimes(eg: 1/x^{2} – 1 is not continuous at 1).
No, 4 is not an algebraic expression because an expression should have at least one variable and one operation to be algebraic.
There are three basic types of algebraic expressions. They are: