# Algebraic Expressions

__Constants and Variables__**:**

The height of a tree is meters long and it grows cm in a year.

Then its height after one year = meters cm

Its height after years = meters cm

Its height after years = meters cm

Its height after years = meters cm

Where represents an unknown number. From the last line, we can find height of the tree after a certain number of years by taking equal to that number. For example, we simply let , and . Thus, the value of depends on our choice. We can give any value or number we want. In other words, the value of is not fixed, it varies from one situation to the other. Therefore, we call a variable whereas is a fixed number whole value does not change. So therefore is called a constant.

__Example__:

Suppose a car covers a distance of km in an hour.

The distance covered by a car in hour = 20 x 2 km

The distance covered by a car in hour = 20 x 3 km

The distance covered by a car in hour = 20 x km

In 20 x = 20, is a constant and is a variable, because can be given any value. It is customary to denote a variable by either or and a constant by or .

__Algebraic Expression__**:**

An algebraic expression is obtained by combining constants and variables by means of the operations of addition, subtraction, multiplication and division.

Examples of algebraic expressions are:

In the first three expressions is the only variable, while in the fourth expression , and are the two variables. Likewise is an algebraic expression with three variables, and .

__Terms of an Algebraic Expression__**:**

The signs “ ”, “-” separate the algebraic expression into its terms, for example:

(1) has one term-

(2) has two terms- and

(3) has three terms- , and

(4) has three terms- , and

__Coefficients and Degree of an Algebraic Expression__**:**

Consider the algebraic expressions and

In , is called the base, 2 is called the exponent of the base , while 5 is called the coefficient of . Exponents tell us how many times the base is multiplied by itself.

For example by we mean , and so on.

In , is the base, is the exponent and is the coefficient of . In , is the base, is the exponent and is the constant before the variable is the coefficient of .

Now consider the algebraic expression; the highest exponent of occurring in the expression is , and we call it an algebraic expression of degree . Note that we will learn in later sections that a number whose exponent is zero is equal to one; thus we can also write . Hence has the three terms and , which have the coefficients , and . The coefficients of an algebraic expression are the same as the coefficients of its terms. Thus, the coefficients of are , and . is also called a constant term.