 For the last little while we're doing the difference of squares just factoring the difference of squares which is Factoring any two things subtracted from each other, right? So if we have If you have one thing minus another thing we can straight up factor this It's just the square of the first minus the square of the second all of the times the square of the first What's the square of the second or vice versa, right? Plus or minus can be switched around That's just straight up factoring and factoring. It's just a way for us It's just a tool that we have to be able to solve equations and equations are basically models or Questions that we have right? So if you want to turn this into a question an equation, right? All we do is say this minus this equals something else for right now. We're just gonna say equals zero, right? So as soon as we have this right now, this becomes a question in mathematics, right? This line is or a statement in mathematics. This line is another thing equals zero, right? Now if we go back to solving our equations or how to mess around with the equal sign which is series 3a, right? What we can do is just grab the pink box and move it over to the other side, right? So what we have now This becomes either a question or a statement for us, right? This becomes the green box equals the pink box, right? And boxes in mathematics in that the way we're gonna use this symbol right now is the box means you could put anything in there, right? It could be a gigantic function function or it could be just a simple variable like x squared that box the same thing It could be a gigantic function or it could be a variable or a number same here. You could put a number here as well so in this case When we start talking about things like this in general As soon as I hit this point with most of my students for me anyway This was this was a huge aha moment for me where The difference of squares kicking it into factoring the difference of squares kicking it into Equations solving for equations for me made me realize that Overdoing is trying to see if something equals another thing or when this equals this or making a statement saying that this Equals this at a certain point, right? So for example initially we one of the first questions we did was x squared minus four, right? The first things that we did was just x squared minus four. We factored out, right? So what we're gonna do now is just turn this into an equation and go equals zero So if you're gonna factor this just because So we've got x minus two times x plus two is equal to zero and we set each one equal to zero So it's just gonna be right So we got x minus two is equal to zero and x plus two is equal to zero and all you do just grab this bring it over Grab that bring it over, right? So all we're gonna have is just x equals two and x equals negative two So that's gonna be your answer to this question. Okay now we're talking about we're talking about the quadratic equations, right? And x squared is a quadratic equation. It's a this thing is a parabola, right now What happens? Let's move the negative four over and take a look at what happens and another way that you can solve for this and it gives you a You know it gives you a certain understanding of and what we're gonna do is graph this as well It gives you a certain understanding of You know what what it is that we're actually doing and it changes the formula a little bit It changes the equation a little bit So all we're gonna do is just move the four over and just see see what what solution that gives us So let's do that same question, but moving the four over. So what's gonna happen is Now when it comes to solving equations We already talked about this and there's two ways that you can solve for this One way is grabbing a four bring it over and it turns it into x squared minus four equals zero And we just did that one. So what you could do is just factor that right? So you factor it out and you get you know your x equals two and x equals negative two, right? The other way you can solve for this is all you need to do is do the opposite Of what is being done to it, right? So if this is square you take the square root of both sides Right the square root of x square is just going to be x x is equal to the square root of four is Most people will say, you know, if you ask anyone what the square root of four is they're going to say it's two Right, but that's only half the answer. The square root of anything is plus or minus So square root of four is going to be plus or minus two So there's actually two answers to this the reason for that is Two times two gives you four and negative two times negative two gives you four, right? And we talked about this in series to it. So the answer to this is plus and minus two So x equals positive two and x equals negative two and that's the same answer that we got when we did the factoring version of this, right? Now this when we set this question up when we had x squared is equal to four Graphically this has this has uh, you know, you have to visualize it. This has a certain meaning Okay, now let's graph this just to explain what it is exactly that we're doing here