__Constants and Variables__**:**

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

Then its height after one year = meter cm

Its height after years = meter cm

Its height after years = meter cm

Its height after years = meter 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 value of depends on our choice. We can give to , the value or number, which we want; in other words 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, therefore is called a constant.

__Example__:

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

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

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

The distance covered by car in hour = 20 x km

In 20 x = 20, is a constant and is a variable, because can be given any value, which we may like. 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 of these expressions, is the only variable while in the fourth expression , and are the two variables. Likewise is an algebraic expression in variables, and .

__Terms of an Algebraic Expression__**:**

The signs “ ”, “-” separates 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 . Exponent tell, how many times the base is multiplied with 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 , the constant before the variable is the coefficient of .

Now consider the algebraic expression, the highest exponent of occurring in the expression is , we call it an algebraic expression of degree . Note that we will learn in higher 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 coefficients of are , and . is also called a constant term.