Constants and Variables:
The height of a tree is 10 meters long and it grows 1cm in a year.
Then its height after one year = 10 meter + 1 cm
Its height after 3 years = 10 meter + 3 cm
Its height after 6 years = 10 meter + 6 cm
Its height after  years = 10 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  = 15, 25 and 55. 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 10 is a fixed number whole value does not change, 10 therefore is called a constant.
Example:
Suppose a car covers a distance of 20km in an hour.
The distance covered by car in 2 hour = 20 x 2 km
The distance covered by car in 3 hour = 20 x 3 km
The distance covered by car in  hour = 20 x  km
In 20 x  = 20 , 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 3 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 2
(3)  has three terms  ,  and 7
(4)  has three terms  ,  and -10
Coefficients and Degree of an Algebraic Expression:
Consider the algebraic expressions 
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, 4 is the exponent and 7 is the coefficient of  . In  ,  is the base, 7 is the exponent and 10, the constant before the variable  is the coefficient of  .
Now consider the algebraic expression  , the highest exponent of  occurring in the expression is 2, we call it an algebraic expression of degree 2. 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  , which have the coefficients 3, 4 and 6. The coefficients of an algebraic expression are the same as the coefficients, of its terms. Thus coefficients of  are 3, 4 and 6. 6 is also called a constant term.
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