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What is a variable in algebra?

Last Updated : 02 Nov, 2021
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Algebraic expressions are build-up by the combination of coefficient, integers, variables, constants, and operations. Expressions are the combination of numbers and letters to form an equation or formula. In these expressions, the real number is the fixed known values whereas, the letters represent the unknown values. The combination of coefficient, variable, or constant and operation is known as the term. 

Types of Algebraic expressions

With the combination of variables, constant, mathematical operators, etc. an algebraic expression is formed. There are majorly three types of algebraic expressions. They are monomial expressions, binomial expressions, and polynomial expressions. Lets take a look at them in detail,

  • Monomial expression

Monomial expressions are algebraic expressions having only one term. For example: 5x is a monomial expression with coefficient. 5 and variable x.

  • Binomial expression

Binomial expressions are algebraic expressions having two terms. For example, 5x – 2 is a binomial expression with 5 as a coefficient of x, x as a variable, and -2 constant.

  • Polynomial expression

Polynomial expressions are algebraic expressions having more than two terms. For example, ab + bc + ca is a polynomial expression with three terms.

Components of an algebraic expression

As seen in the examples above, there are different components involved and are part of algebraic expression. The components are coefficients, variables, and constants. Lets take a look at their definitions,

  • Coefficient: The fixed values attached to the variable (an unknown value) are known as a coefficient. For example: In 2x – 4 is an expression having 2 as a coefficient of x.
  • Variable: The unknown values represented by letters in an algebraic expression are known as variables.
  • For example: in expression 5x + 1, x is the variable.
  • Constant: Constants are the fixed real numbers in the expression combined with an operation. Constants are not attached with variables. For example: In expression 4y – 3, -3 is a constant.

What is a variable in algebra?


An algebraic expression is built up by terms. In terms, we deal with coefficient, variable, constants, and operations. 

In the expression, 9y – 1

9 is the coefficient of variable y.

y is the unknown value or variable

-1 is the constant 

And, the expression consists of terms. It means it is a binomial expression.

Variables are the unknown values of the expression. They are represented or assumed by letters. Variables always come attached with a coefficient. There are various equations to solve these expressions and get a solution for these unknown values.

Sample Questions

Question 1: What is a variable expression?


The expression that consists of variables along with numbers and operations is variable expression. For example: 2x + 3y, 5y + 3, etc.

Question2: What are numeric expressions?


The expressions consist of numbers and operations but do not include variables. For example: 2 + 10, etc.

Question 3: List the types of polynomials?


  • Linear polynomial
  • Quadratic polynomial
  • Cubic polynomial

Question 4: What are the variables in equation 2y – 3x?


y and x are the variables in the equation and 2 and 3 are coefficients of these variables respectively.

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