Okay, welcome. Welcome to this section on algebra. And this is what we're going to cover in this section, literal numbers. And if you don't know what I mean by that, just hang on we'll get there. Powers and roots of literal numbers multiplying and dividing literal numbers with exponents, fractions with literal numbers, terms and factors, polynomials, canceling little numbers in a fraction, and simplifying expressions using factoring and canceling. Alright, so we're going to cover these and just stay with us on this and don't don't get a little no anxiety.

Just because it says algebra here. We'll get through it. Alright, see on on the next slide. Okay, so what do we mean by literal numbers? Well letters, such as a, b, x, y, and so forth. We could use def, whatever are used as literal numbers.

And we use these literal numbers where we can assign a value. So for example, if I say A equals three, and I say, okay, what's to a? Well we know to a is six. All right? And we have different ways of representing literal numbers. So for instance, over here, when I say A, A, B, that is A times B.

When I say To a, it's two times a. When I say A plus A, it's two a. When I say A times A, it's a squared. And if I take the square root of one for this example here, a squared, what's the square root of a squared? That will be a one over a is one divided by A. Okay?

And again, we're using a here is an example. But that a could be any number. I could have changed that to B or x or whatever, and it would be the same. So let's just clear the slide here. So what I'm saying is, even though I'm using a here, I could substitute a for B x, y or whatever literal number I'm using. All right.

Okay. By using this as an example, I want you to give me a true and false on these these little exercises here. So for instance, if I say, six A B, is that the same as saying six times a times b, so you're going to give me a T or an f, t for true, false. And I'll give you this one. It's, it's true. Okay, let's do the next one.

And then I'll leave the rest to you. C cubed, is that C times c times C right here. Well, if you go back when we talked about squaring square roots, Yeah, it is. So what we're doing right here isn't Instead of using a number, we're using what we call a literal number, which is represented by a letter ABCD, F, G, whatever. All right, try to do the rest of these. And guess what, as always the answers on the next slide, see over there, take a few minutes into it.

Okay, here are the answers for you right there. And there's the answers. I'm not going to call them out. Obviously, T's for true and false. Again, if you have a problem with them, go back review the information. And as always, in the first slide, you have a number.

Okay, you also have an email that you can contact me through this platform, give me a call, we'll set something up. And there you go. So take a look at them. And let's go on to the next slide. Okay, we We're still talking about literal numbers now, but we want to add or subtract literal numbers. Basically, if, if the literal number is the same, we just add them.

So for instance, on this first example, I have five a plus two a. All right? So because they're, they both have the same literal number, in this case, a, I just add them. So five plus two is seven. We got a, okay, A is the same. So it's seven, eight.

All right, when we want to subtract, it's the same deal. Five A minus two a, five minus two is three. And a is a common literal literal number between them. So my answer is three, eight. But let's look at this one here. This one's a little different now.

We have five a plus two A plus two B. What's different the two B, so I can't combine that. However, I can combine the five a and the two a right here. And what do I get? I get seven a, and I just bring over my two B. So my answer for this one is seven, eight plus two, B.

Okay? So take a look at them, and again to reinforce that, okay, here's some exercises. Take the time doing them. All right. I'm going to pick two to do for you. dddd let's pick.

Let's pick six y plus y. What is that? That's seven y. And what do we got over here? Well, let's do let's do this one to a plus three. C plus three a well what would that be?

What's common? My two A's a common, right? So I've got five a, make it a little smaller five a plus three C. All right. So it's five a, because I add the two and the three is five plus three. See? That's it.

Let me just let me stop here. Reset, make it look. So here it is five, eight, plus three. See, that's the answer, right? Take a few minutes. Do the rest of them.

And then as always, I keep preaching it, you know where the answers are on the next slide. So we'll see over there. Okay, again, here are the answers there right there. It's pretty self explanatory again, with just Substituting a letter for a number. And we can we can assign any value to that literal number, whatever it is ABCD and so forth, which which we're going to do is when we get out a little further, but here are the answers, take a look at them. Again, if you have a problem, send me an email, call me.

If you're in the continental United States, I will return the call if you're out then send an email, we'll set something up via email. Alrighty, with that said, let's go on to the next slide. And we'll see over there. Okay, well, again, on this slide here, we're talking about powers and routes of literal numbers. And let's look at the examples that that I've given you. As I say, here, an exponent is used in the same way with literal numbers as with decimal numbers.

If you look at this example here, a squared equals A times A and A cubed is A times A times A times A. All right? Same deal. When the num when the letter has a numerical coefficient included with the literal base both raise to the higher power. So for instance, right here, okay, I've got three A squared, that whole term, and that's called a term. Now three a is called the term.

Okay, that whole thing is squared. So I break it up. I square the three and i square the A, and I get a nine A squared. Okay, let's clear the slide off here. And go to the next bullet. Okay, when an exponent of a literal number is raised any power, the two exponents are multiplied.

So for instance, I have a squared and I want to cube eight square, so all I do is multiply the exponents. In this case two times three, two times three is six. So my answer is A to the sixth. Okay? So that should be pretty straightforward. we've kind of gone through this previously, when we were just talking about powers and routes with with with just numeric values in there and not with literal numbers.

Again, the only thing we're doing is was substituting a letter in there for a number. Okay, let's look at this here. And just remember the rules. I gave you up there. And if you apply these rules to this, you should get the correct answers. And again, the correct answers are in the next slide.

So we'll see you over there. Okay, so here are your answers. And take a look at them again, apply these rules. And you shouldn't have a problem. But if you do, give me a call, send me an email, we'll help you out. And and the other one other thing and I preached it before, any number to the zero power is one.

So this one might be a little tricky. So A to the zero is one. And if I q one, one times one times one is one, got it? Okay. see on the next slide.