 So this is part three of factoring, and in part three we're going to look at difference of squares. So in the difference of squares, when we talked about conjugate pairs, we had like A plus B, A minus B, like this, and the outside terms were negative AB, and the inside terms were positive AB, so they cancelled each other out. Because they're opposite signs here, but the exact same numbers, they drop out the middle term, and we're left with this perfect square, A times A and B times B. So we need to figure out what the A's are and the B's are and so forth. So I want to look at this one, and I'm going to let Y to be X squared, in fact we could put that in our calculator and look at the table here if we wanted to, X carat two, and then we're going to go look at our table, and when one is squared we get one, when two is squared, my table over there says four, when four is squared I get sixteen, notice I've skipped some, but these are the most common ones, but sometimes you forget what they are, six times six would be thirty six, and if I keep scrolling down here, I get seven, it would be forty nine, nine would be eighty one, and ten would be one hundred. So if we're looking in this column, this is like our A squared or our B squared, these numbers would be our A squared or B squared, and this column would be our A's or our B's. So when we're looking at X squared minus nine, X times X is always going to be X squared, so A is always going to be X there, but I have a nine, and if I look over at nine I don't have it there, but I can look at my table and my calculator, when Y was nine it said that X was three, so three is my B, and so all we have to do is write our first terms because factors are the first term, our first terms, so my X and my X factors are the last term, that's my three and my three, and then we do our opposite signs, and we're done factoring, these are really quite nice. So let's look at this one, I wanted to remind you that we need to always look for a greatest common factor, and in this case we have one, it would be four. So we have four, our greatest common factor, times X squared, and four times nine is 36, so X squared minus nine. Now I have two terms, okay this is key, I have two terms, and is it a difference of squares? Can't be a sum, but is it a difference of squares? Well if you look at that very carefully, this is a perfect square, and nine is a perfect square and we're subtracting, so yes it is, so I have to carry along my four, but now I'm going to find out what my A's and my B's are, so I can fill in X squared, and A is going to be X, and nine, that tells me that B is going to be three times three, so my X's are my first terms, and my threes are my last terms, and the only thing I have to do is make one a positive and one a negative so that my middle terms will fall out, and there I have a very colorful solution. So back here, do we have a greatest common factor? 16 and 25 do not have anything in common, so I don't have to worry about that, I just have to think, okay 16 X squared, then my A is going to be, I know it's X, but I've got a number in here, so I come back over to my calculator and when I have 16 it tells me over here that my A must be the four times X, and on square both of those we get four X. My B would be 25, which says it's, B squared is 25, so B would be five, so here we go, first terms are four X and four X, last terms are five and five, one of them has to be positive and one of them has to be negative, and we're done factoring, and we're done factoring literally, so I want to take some time to think about a strategy, I think we have some time here, strategy, step one is always find the greatest common factor, step two is find the number of terms, because we factor different types of problems differently depending on the number of terms, if there's two then you have to ask yourself is it a difference of squares, if it is you can go further, if it's not you're done, but you might have three terms, okay, with three terms we're going to factor those with the A, C or box method, and the X, A, C, and B, and then we might also have the possibility that we have four terms, and when we have four terms remember that's where you take the first two terms, and the last two terms, and find the greatest common factor, and then you also, then you take the greatest common factor of the two term result, and then the last up in our strategy then would be just to check the factors one more time for our greatest common factor, sometimes we don't catch it in the very beginning, but it will be in the end, that's here's an example what I'm talking about, if I had like 2x plus 4 with x minus 3, well 2x minus, or 2x plus 4 has a common factor in it of 2, so then I need to factor that out, and I'd have x plus 2, and then our x minus 3, this would be the completely factored form.