 The simplest difference of square there is that usually everybody starts off with this is you have if you have x squared minus four you can factor this out and I usually put the two brackets first for summaries and I don't know I'm just like filling it in I guess but it's the square of the first guy minus the square of the second guy and square root of x squared is just x right and if you do not know your exponents and radicals stop right now and go to series two two and I can honestly tell you the the place that destroys most people that I've seen that stops most people from that I've seen from progressing any further in mathematics it it's exponents and radicals that's why I spent I did a whole series on it okay usually when I get a brand new student I start with a real number set and when we start working things through it's exponents and radicals that we hit us we hit a snag that they don't know that I have to sit there and review the whole thing and that includes grade 12 that I've had that includes university students that I've had okay for summaries and exponents and radicals destroys people it's simple it's just a different level right and we talked about this this is the principal level and just kicking up another level and in mathematics when you have your base number here or base variable here you can put symbols all around and there are symbols that will all around this base level that they mean something right and the first place you go to is to the exponents when you're going beyond just simple mathematics where you're dealing with just one level of math one level of numbers or variables right anyway that's digressing so if you don't know exponents and radicals series two squared of x squared is just going to be x so you can just go x here and x here because they're both the same thing so whenever you're taking the square root here whatever you put here that's going to be the same thing here and that goes for this as well square root of four is just going to be two and two right and all you do is just go plus minus or minus plus doesn't make a difference I'm going to switch them up between plus and minus minus and plus as long as they're different right let's do a few more questions so you could have you know variables and numbers mixed together right you could have you got four x squared minus nine y squared and again it's just the square root of first one minus the square root of second one square root of first one plus the square root of second square root of four x squared it's just going to be two x square root of nine y square it's just going to be three y so two x your choice minus or plus let's go minus two x minus three y times two x plus three we did straight up numbers straight up variables variable number so let's do fractions right fractions work the same way four x squared divided by 25 minus nine divided by y squared and fractions again you take the square root all you do is just take the square at the top and the square at the bottom so the bottom stays where the bottom is right some people when they take square roots of these things lately for some reason the denominator goes up to the top which is I'm not sure how that works but whatever you're factoring in the bottom stays in the bottom so all we do I'm just going to put my brackets down first four x so four x squared divided by 25 the square root of that is just going to be two x divided by five right and so it's going to be two x divided by five here and two x divided by five here squared of nine over y square it's just going to be squared of nine is three divided by squared of x of y squared it's going to be one right so three divided by one and your choice plus minus minus plus just make sure you switch any two things subtracted from each other you can factor right so let's just start off with this fairly simple it's x to the power four minus y to the power four if we're going to factor this it becomes right so it becomes x squared minus y squared times x squared plus y squared right now again any two things subtracted from each other we can factor so we can continue factoring this one right actually we can continue factoring this one forever really but we're going to stop as soon as we get to x and a y because the whole point of mathematics the whole point of just algorithm just trying to factor is trying to simplify mathematics not to not to make it harder so at a certain point you're going to have to make a decision to stop because you can't go any further right or you can't go further but it's not going to make your equation or your expression simpler so this guy we can factor further this guy we can't factor further because two things added together we can't factor so if we're going to factor this guy x squared minus b squared x squared minus y squared y squared it's just going to be x minus y times x plus one this one is going to stay the same so we need we're going to have three brackets on this row so this one factored out into x minus y x plus y and that one just stayed the same so it's x squared plus y squared and this if you're going to factor this guy this guy fully factored this here if you only take it to here if the question is worth one mark you're only going to get a half mark you've only got half the job and from here you can't do this any further because now you're going to have the squared of x minus the square root of y times the square root of x plus the square root of y times that times that so and then that one is going to have a minus during the negative but you don't want to do that it just makes it too complicated now all the expressions you get through factor they mean they may not factor properly they may not factor you have breakdowns so simply right or they may not break down at all but you still want a factor of to be able to solve your equation of equations and we're going to go with this right so you might get some kind of expression like this so let's say you just have x squared x squared minus 13 now this one you can still factor right even if you had a y here you could factor it doesn't make a difference you can have anything on this side you can factor right so you could have if you're going to factor this you just square root of 13 why because squared of 13 that's a prime number you can't break that up and why it's just why you can't take that outside of your root symbol right and again series two so you got x squared of 13 let's do a large large expression something silly that we're not really going to get initially anyway but let's just see how it breaks down if it is large something that doesn't factor something that's you know got fractions in it okay i have to write this down because uh there's no way i was going to remember and do it properly so all this is the way you do this is is to square the first one minus the square of the second one times the square of the first one plus the square of the second one right so let's just do this hopefully you can read this the wall was not cooperating it's got a bump on it so the truck is not sticking to it um anyway squared of 16 x squared over w squared z to the power of eight it's just going to be four x divide by z uh w z to the power of four same uh same thing on the other side so that's what we have over here and squared of squared of 15 now you're not going to get anything like this right anything silly like this hopefully you won't get anything silly like this but if you do get something like this all it is it's just squared of the first one you put minus the square of the second one times the square of the first one plus the square of the second one and this is where series two comes in we're super important no series two because series two is about taking square roots of things either variables or numbers with numbers you need to break them down to their prime uh prime factors with with variables all you got to do is just figure out you know x cubed means there is three q's in there so if you're going to take the square root you're looking for pairs pairs can come out of signals right and talk a lot about this in series two so again if you haven't if you don't know your exponents if you don't know your radicals you need to stop right now and what you need to do is take a look at series two and you need to become really good at that okay hopefully you'll you've got the gist of it you understand that just two any two things subtracted from each other you can factor and you can group things together right