What are Algebraic Expressions? Explain

Algebraic expressions are the equations we get when mathematical operations such as addition, subtraction, multiplication, division, etc. are acted upon by any variable. For instance, let us believe that Ron and Tom were playing with matchsticks and thought of forming number designs using them. Ron took four matchsticks and formed the number 4. Tom added three more matchsticks to form a pattern with two 4’s. They both realized that they can keep on adding 3 matchsticks in every step to make one extra four. By this, we concluded that they need 4+ 3(n-1) approximately sticks, in general, to make a pattern with ‘n’ number of 4’s. Here, 4+ 3(n-1) is termed as an algebraic expression.

What are Algebraic Expressions?

An algebraic expression or variable expressions is a mixture of terms by mathematical operations such as addition, subtraction, multiplication, division, etc. For instance, let us have a look at the expression 5x + 7. Therefore, we can say that 5x + 7 is an illustration of an algebraic expression. There are various elements of an algebraic expression.  In this blog, we are going to explore the basics of algebra.

Variables, Constants, Terms, and its Coefficients

In arithmetic, a symbol that doesn’t have a determined fixed value is called a variable. It can use any value on the number line. In the above illustration that involved matchsticks, n is the estimated variable and in this case, it can take the values 1,2,3,… A few examples of variables in Math are a,b, x, y, z, m, and many more. On the other hand, a type that has a fixed numerical value is termed a constant. All numbers existing in the number line are constants. Some cases of constants are 3, 6, -(1/2), √5, and so on. A term is a variable alone or is a constant alone or can be a mixture of both variables and constants by the mathematical operation of multiplication or division. Some samples of terms are 3×2, -(2y/3), √(5x), and so on. Here, the numbers that are multiplying the given variables are 3, -2/3, and 5. These numbers are termed coefficients.

How to Simplify Algebraic Expressions?

To simplify an algebraic expression, one just needs to combine the like terms. Hence, the like variables will be unitedly combined. Now, out of the like variables, the same powers will be again unitedly combined.

Algebraic Expression Formulas

Algebraic formulas are the stated original short formulas that help students to solve the equations easily, accurately, and effectively. They are just a rearrangement of the presented terms to create a better expression that is easy to memorize and faster to solve as well. Below is given a list of some of the fundamental and primary formulas that are being used widely and commonly. Have a look at these given formulas to understand the algebraic formulas better and easily. 

  • First one: (a + b) = a2 + 2ab + b2
  • Second one: (a – b) = a2 – 2ab + b2
  • Third one: (a + b)(a – b) = a2 – b2
  • Fourth one: (x + a)(x + b) = x2 + x(a + b) + ab

Types of Algebraic Expressions

The primary and main types of algebraic expressions are based on the number of variables found in that particularly given expression, the number of the terms present in that particularly given expression, and the values of the exponents of the variables in every individual expression. Given below is a list that divides the algebraic expressions into five main and primary different categories. Let us have a look that will make algebraic expressions easy to understand and grasp.

  • Monomial
  • Binomial
  • Trinomial
  • Polynomial
  • Multinomial


Algebraic expressions need a solid foundation to be set in order to move onto complex mathematical problems and concepts. It is very important for students to effectively understand the working and the properties of algebraic expressions. In order to strengthen your fundamental concepts of algebra, you can solve Cuemath interactive worksheets that are free to download. These worksheets allow students to practice concepts and explore the topics in the most engaging and interesting way.