## How are expressions formed?

We know very well what a variable is. We use letters x, y, l, m, … etc. to denote variables. A variable can take various values. Its value is not fixed. On the other hand a constant has a fixed value. Examples of constant are: 4, 100, -17, etc.

We combine variables and constants to make algebraic expressions. For this we use the operations of addition, subtraction, multiplication and division. We have already come across expressions like 4x + 5, 10y -20. The expression 4x + 5 is obtained from the variable x, first by multiplying x by the constant 4 and then adding the constant 5 to the product. Similarly, 10y – 20 is obtained by multiplying constant 10 with variable y and then subtracting 20 from the product.

The above expressions were obtained by combining variables with constants. We can also obtain expressions by combining variables with themselves or with other variables.

Look at how the following expressions are obtained:

x2, 2y2, 3x2 – 5, xy, 4xy + 7

• The expression x2 is obtained by multiplying the variable x by itself;
x x x = x2Just as 4 x 4 = 42, we write x x x = x2. It is commonly read as x squared. In the same manner, we can write
x x x x x = x3

Commonly, x3 is read as x cubed which can also be read as x raised to the power 3.

• The expression 2y2 is obtained from y: 2y2 = 2 x y x y
Here by multiplying y with y we obtained y2 and then we multiply y2 by the constant 2.
• In (3x2 – 5) we first obtain x2 and multiply it by 3 to get 3x2. From 3x2, we subtract 5 to finally arrive at 3x2 = 5.
• In xy, we multiply the variable x with another variable y. Thus, x x y = xy.
• In 4xy + 7, we first obtain xy, multiply it by 4 to get 4xy and add 7 to 4xy to get the expression.