The same rules apply to adding and subtracting
monomials that apply to integers. We also call this "combining"
monomials.
We can only combine terms that
are exactly alike!!!!
(In other words, the variables, if any, must be exactly the
same. If one term's variable has an exponent and the other
does not, they are not like terms.)
Examples of like terms are:
5x and 7x
4p and 9p
3y² and y²
10 and 14
These
are not like terms:
6x and
4y
2ab and 3cd
8x and 9x² 
To combine monomials, we must remember two important
rules:
If the
signs are the same, add and keep the sign.
If the
signs are different, subtract and keep the sign of the larger number.
Let's combine these terms:
5x7x
(remember the "" sign is attached to the 7x making it a
negative)
The signs
are different so we subtract the two numbers (75) and keep the
sign of the bigger number (the negative since 7 is larger than
5). We then attach the "x".
So... the
answer is... 2x 
Let's look at a few more.
4p+9p = 5p
We again subtracted the integers since we had
different signs and took the sign of the larger number. 
3y² y² = 4y²
If there is no integer
before a variable, it is understood that there is a "1" there.
So this can be thought of as 3y²
1y². We add the integers since they have the same signs
and keep the negative in our answer. 
10  14 = 4
Although there are no variables involved, these integers are
like terms. Since the signs are different we subtract and
keep the sign of the larger number. 
Let's take this lesson to the
next level...
