Adding and Subtracting Polynomials
A polynomial looks like this:

example of a polynomial
this one has 3 terms 
To add polynomials you simply add any like terms together .. so what is a like term?
Like Terms
"Like terms" are terms whose variables (and their exponents such as the 2 in x^{2}) are the same.
In other words, terms that are "like" each other.
Examples:
Terms 
Why are they "Like Terms" 

7x 
x 
2x 
because the variables are all x 

(1/3)xy^{2} 
2xy^{2} 
6xy^{2} 
because the variables are all xy^{2} 
Adding the Polynomials
Two Steps:
 Place like terms together
 Add the like terms
Example: Add 2x^{2} + 6x + 5 and 3x^{2}  2x  1
Place like terms together: 
2x^{2} + 3x^{2} 
+ 
6x  2x 
+ 
5  1 






Add the like terms: 
(2+3)x^{2} 
+ 
(62)x 
+ 
(51) 
= 5x^{2} + 4x + 4
Here is an animation to show you:
(Note: there was no "like term" for the 7 in the other polynomial, so we didn't have to add anything to it.)
Adding in Columns
You could also add them in columns like this:
Adding Several Polynomials
You can add several polynomials together like that.
Example: Add (2x^{2} + 6y + 3xy) , (3x^{2}  5xy  x) and (6xy + 5)
Line them up in columns and add:
2x^{2} + 6y + 3xy
3x^{2}  5xy  x
6xy + 5
5x^{2} + 6y + 4xy  x + 5
Using columns helps you to match the correct terms together in a complicated sum.
Subtracting Polynomials
To subtract Polynomials, first reverse the sign of each term you are subtracting (in other words turn "+" into "", and "" into "+"), then add as usual.
Like this:
Note: After subtracting 2xy from 2xy we ended up with 0, so there is no need to mention the "xy" term any more.
