 Two things subtracted from each other. They can give that to you in multiple different forms. And later on, once we're done with all the different types of factoring techniques, I'm going to go through probably to, you know, sit down and take like at least 20, 30 different types of factoring questions. And I'm going to factor those out using, you know, all the different factoring techniques, the manual factoring techniques, right? So I'm not going to, I'm not going to do too many more examples with fact with the difference of squares right now. But one type of, one type of factoring question that they give people, or have seen appear a lot is basically, it doesn't look like it's two things subtracted from each other, but it is two things subtracted from each other. So one thing, the simplest version of is the following. Sometimes they let you give me a question like this, which is this is x minus five, all squared minus 16, right? Now, if you've done enough problems like this, you know that this is just two things subtracted from each other. Like we said, any two things subtracted from each other, you can factor. So all it becomes is the square root of this guy minus the square root of 16, the square root of this guy plus the square root of 16. Now the square root of x minus five all squared, that's just going to be x minus five, right? Square root of 16 is four. So it's going to be x minus five, that's if you want, if this confuses you that, you know, that this is now two terms, what you can do is put, you know, brackets around here and realize that that's just the square root of that guy, right? But square root of x minus five all squared is just x minus five, square root of 16 is just four. Close your bracket and square root of x minus five all squared is just x minus five again and square root of 16 is just plus Now, this question, you need to take it one more step further because combine your fives and fives and fours here, right? So this becomes x minus five minus four, negative five, the sign in front of the number goes with the number. So negative five minus four is going to be negative nine, so that's just going to be x minus nine and that's going to be negative five plus four. Negative five plus four is going to be negative four. Confused myself, but I have two negatives here, right? But you can't have two negatives because these two numbers, if you combine them, you got a negative number. So this just becomes x minus nine times x minus one and that's that guy factored. Let's do the reverse of this, we have 16 up front and minus x minus five all squared and something changes when you do that and that goes back to when we were dealing with negative numbers. If you have a negative number in front of a bracket in front, you know, brackets where there's multiple terms in there, that negative sign is going to apply inside all the terms inside the bracket. So let's just flip these guys around and see what happens there. So let's flip the last one and see what happens where the special rule where you apply the negative sign inside the bracket comes in, right? So all we've done is just flip the two numbers around. We've got 16 minus x minus five all squared, right? Where x minus five all squared. So it's just going to be the first term minus the square root of the second term, square root of the first term plus the square root of the second term. But one thing we're going to have to be careful of is the negative sign minus the second term, that negative sign is going to apply both x and to the negative five. So what we're going to do when we square root that square root this term, we're going to put our brackets in there. Now the more of these you do, the less you need to use the brackets. I personally use them a lot because I don't want to remember where what sign has changed to what. I just, I would rather just do another term, just follow up with another line and remove the brackets there, okay? Because I ended up making a lot of silly mistakes when I just do, you know, when I try to solve a lot of problems when it came or when it comes to tests, right? You end up, we're human, right? We end up making mistakes. To eliminate mistakes, we use the symbols, okay? We don't skip the steps. So let's just do this. So what we got for the first one, the square root of 16 is just four. So four minus the square root of x minus five all squared is just going to be x minus five. But because we have a negative sign right there, that negative sign is going to apply to the x and the negative five, right? So I put the extra brackets in there because that's going to remind me for the next line to apply the negative sign going inside the brackets. And whenever you have negative bracket, that basically means that's negative one, right? You could have had a number in front there, right? You could have had, that could have been a four there and square root of four would have been two. So the negative two would have been applied. We didn't have a number there. So it's just means that negative one's being multiplied in. For that line, that's just good. That's square root of 16 is four plus the square root of five minus x minus five all squared. Now the plus sign, that's just plus one going in. So the signs don't change. The x stays the same and negative five stays the same. So for the positive one, whenever you encounter something like this, for the positive one, you don't need those brackets there because whenever you have a positive sign in front of brackets, the signs don't change. If there was a number there for sure, you got to put the, you should put the brackets and multiply them in there, right? So the next line, we're just going to eliminate those brackets, the double brackets that we have and we're going to see what we have. So what we got on the next line is four minus x because negative one, bring in, bring it inside the bracket. Negative times x is going to be negative five. So four minus x plus five and the other side just stays the same, just four plus x minus five. So what we can do now is just combine the numbers together, add them together, right? And four plus five is going to be nine and over here we've got four minus five is going to be negative one. So what we ended up with is nine, four plus five is nine, nine minus x. And over on this side we've got four minus five is negative one and we've got an x. So I got x minus one. Now you could have written the bottom as negative one plus x, right? But I usually don't like the first term when it comes to brackets if I can help it anyway. For the first term to have a negative there because that sometimes gets lost in the shuffle, right? So I like the first term with the brackets as a positive. That way I don't have to worry about that term there, right? So I usually end up putting the negative as a second term or the third term or fourth term whatever it ends up being, right? So for the factor of the 16 minus bracket x minus five all squared, factoring that we end up with nine minus x times x minus one, okay? And that answer is different from what we got before when it was x minus five squared minus 16, right? Because the negative sign flipped things around for us.