4.1 Addition and Subtraction
Adding variables isn’t difficult. Here below you see a quadrangle with different length for each side. 
Example А: 

The expression for the quadrangles perimeter is written as:
Perimeter: 5f + 4f + 3f + 2f = 14f 

Example B: 

If we are to express the perimeter for the figure above then it will look like this:
Perimeter = 3g + 2j + 2g + 3 = 5g + 2j + 3
We add the similar terms with each other. So, we cannot add 5g with 2j, because these have different variables which can have different variables. 


Example C:
In three match boxes there are an equal amount of matches, and we write the number of matches in a match box with t. Besides this there are a number of loose matches. 

We write the expression for the total number of mats as:
Number of matches : t + t + 3 + t + 2 = 3t + 5 


We can show that 3a + 5 + a = 4a + 5 by looking at an example with distances. Check it for yourself if it is correct. 
3a + 5 + a 




3a 
5 
a 












4a + 5 

















4a + 5 







When subtracting, the same thing applies.
Example: 4m + 7 – m 
4m + 7  m 

















3m + 7 















Can you add the following terms with variables: a + a^{2} + a^{3} ?
We can test this with the following figures:
 a can be illustrated by a line.
 а^{2} can be illustrated by a square with the side a.
 а^{3 }can be illustrated by a cube with the side a.


Is it possible to add a length with the square or a cube?
The answer is no. We can’t add and simplify these terms. 
