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Variables and Constants in Algebraic Expressions

 

Algebra is a major branch of mathematics which talks about operations, relation and their constructions. Algebra has a very wide range of applications in daily life. It is also considered one of the most fundamental building blocks of mathematics. Algebra deals with binary operations, mathematical relations and constructions of various functions, which plays a huge role in a student’s integral part of education. Apart from that, algebra helps improve the understanding of many other branches of mathematics such as arithmetic, geometry, calculus etc.

The word algebra is derived from an Arabic phrase called “al-jebr”, which means “reunion of broken parts”. It involves the study of various constructions of mathematical figures, explanations and proofs of concepts such as polynomials, algebraic structures and equations.

An algebraic expression is defined as one or more algebraic terms or expressions used to express a different concept. Variables and constants are considered basic building blocks of an algebraic expression and operating symbols, namely plus and minus signs. The following is an example of an algebraic expression containing constants and variables.

5 x2 + 7 y + 8 x y + 4 = 0 

In the above example, 4 is considered a constant that cannot be changed, or if changed, it will give different results, whereas the alphabets, namely “5x 2 + 8xy +7y”, is termed as a variable term.

Algebraic expressions are nothing but a collection of numbers and alphabets separated by plus and minus signs. This article will give a wide overview of an algebraic expression and give an in-depth knowledge of the constants and variables present in an algebraic expression. There are three major classifications in terms of algebraic expressions. They are Monomial expression, Binomial expression and Polynomial expression.

  • Monomial expression: It is nothing but when an algebraic expression has only one term. This single-termed algebraic expression is known as a monomial expression. For instance, 9 x y is a monomial expression.
  • Binomial expression: If an algebraic expression has two terms, then it is termed binomial expression. 5 x + 2 y is an example of binomial expression.
  • Polynomial expression: Polynomial expressions are obtained if an expression has more than two terms with only positive integral elements of variables. 6 x + 7 y + 4 x y = 0 is an example of a polynomial expression.

Constants

Constants are considered as algebraic expressions which only involve numbers. They have termed constants because their value is always the same. No variable can change the value of a constant. For instance, take the number 6. It is a universally known constant number, and it contains a particular value inside, and it cannot be changed. In the following expression, 5xy – 2 = 3y, the second term on the left-hand side is considered as a constant term, and 5xy cannot be considered as a constant term because the x and y values can be varied, which will affect the entire term 5xy.

Variables

In algebraic expressions, letters or alphabets are termed variables. The value of the following terms can be easily changed, 6x + 8y = 0. The x and y values can be substituted for any other number, which affects the terms and the final result. So, they cannot be constants.

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