Adding and Subtracting Polynomials

Hi!
Today I was going to post about dividing polynomials, but I figured it'd be better to start with addition and subtraction first- you use them in division, and they're important to know!
Because I hate typing out variables with indices and because drawing pictures on photoshop takes a long time, I decided to do these by hand... So I apologize if you cannot read my handwriting, or if the colors are a little off.
Also- if you are to be wary of any incorrect information in this post, it's to be wary of the positives and negatives. I occasionally have trouble with them... [awkward cough]

But, without further delay...
Addition and subtraction of polynomials!

To add the polynomials, you can lay them out horizontally and add the variables that way. However, I find that a little difficult, and harder than the second way. The second way is to stack the numbers in a vertical way, and then add down.

Of course, this is where those pesky positives and negatives come in. However, it's not that hard to explain- I even made a picture for you about this as well.

Basically, remember that two negatives equal a positive, and that a negative plus a positive means, basically, the positive minus the number that is negative. (So -14 + 2 can also be phrased as 2 - 14, which is also 14 - 2, only with a negative sign on the end. If any of that made sense...)
Just remember your positives and negatives and you'll be fine.

To subtract two polynomials, you basically turn it into an addition problem.
Here's the picture I drew (I'll explain it more fully after the picture.):

Let's describe what's happening in this picture.

First of all, you have your polynomials. I'm going to simplify these and simply do this problem as an example:

(x + 2) - (2x - 8).

If you look at that, what you really have are two different phrases, attached to each other. (Remember, the positive and negative sign attaches- what looks like a minus can actually be used as a negative.)

Those two phrases are:

+ (x + 2)

and

- (2x - 8).

To transform this, you want to change that negative sign in " - (2x - 8)" into a positive sign. To do that, simply multiply the (2x - 8) by -1 (or simply switch the signs.) This will give you:
+ (2x + 8).
Adding those two together will give you
(x + 2) + (2x +8) =
This also works for negatives- let's switch our negatives/positives around for a second...
(x - 2) - (2x + 8).
Now your two phrases are "+ (x - 2)" and "- (2x + 8)". Again, simply transform the negative sign on (2x + 8)...
You'll then have "+2x - 8". And so on and so forth.

Take another look at my picture now that I've explained all the steps in it...

Does that make sense?

So, really, all you need to remember is how to do addition, and how to turn a subtraction problem into an addition one, and you'll be fine! :)