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6 Algebraic Expressions

Algebra is the branch of Mathematics that generalizes the facts Do you know?
of Arithmetic. An important characteristic of Algebra is the use The study of Algebra began in
of letters of English or Greek alphabet to represent unknown Egypt. A Greek mathematician
numbers or to generalize a result. These letters are called Diophantus, was among the first
mathematician to use symbols to
variables. Algebraic expressions are formed by combining represent unknown quantities.
constants and variables using the fundamental operations of
addition, subtraction, multiplication and division.

In this chapter, we will learn about polynomials, addition and subtraction of algebraic expressions,
finding value of algebraic expression and use of algebraic expressions.

Literals
To deal with problems of finding unknown numbers, some letters of the alphabet are used to

represent numbers. These letters like x, y, ..., l, m, ..., etc. are called literals.

Constants

A quantity having a fixed numerical value is called a constant. Numbers 4, –5, 0, … are constants.

Algebraic Expressions

Algebraic expression is a combination of literals and constants connected by signs of fundamental
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operations (+, –, × or ÷). For example, x , 3x + 5, 4xy – 5, 3x + 4y, etc. are algebraic expressions.

Terms of an Expression
The terms of an algebraic expression are the parts of the given expression which are separated
by a sign of addition or subtraction. In the expression 3x + 4y, the terms of the expression are 3x

and 4y.

Constant Term

In an algebraic expression, a term which has no literal factor is called a constant term. For
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example, in the algebraic expression x + 2x + 1, the constant term is 1.

Variable Term

We know a variable is a quantity which can take different values. A variable term may contain
only literal like x, y, etc. or product of a constant and a literal like 4x, –3y, ... etc.