Welcome back, everyone. In the last couple of videos, we saw how to evaluate an algebraic expression. I could evaluate an expression like this by basically replacing letters with numbers. So if x was 3, I just replace the x with 3 and so on with y. But some problems are not going to have you do that. In some problems, you're going to have to take a long, complicated expression, something that might look like this, and you're going to have to write it in a simpler form. And that's called simplifying an algebraic expression. It's what I'm going to show you how to do in this video. Basically, by the end of this, I'm going to show you a step-by-step process for how something like this expression actually just simplifies down to just a variable x. I'm going to show you exactly how that works. Let's get started. The idea here is that we can take a long expression and write it in a simpler form and that just comes down to reducing the number of terms. So let's talk about what a term is. A term is basically just a part or a thing in your expression that's separated by a plus or a minus sign. So, for example, we have 5 minus x plus 3y plus y. There's a minus sign here, a plus sign, and a plus sign. So all these four things here are parts of my expression. Those are all just terms, and we can see here that some terms are actually just numbers only, like 5. Some of them are variables only, like x and y, and then some of them are actually just combinations of numbers and variables, like 3y. Alright? All these things are terms. Now 2 of these things are more similar than others. And what do I mean by that? The 5 and the x aren't similar because one's a number and one's a variable. The x and the y are 2 different variables, but this 3y and this one y over here, those are similar. And the way I like to think about this is you can imagine an x is kind of like an apple, and a y is kind of like a banana. This expression is saying you're going to minus an apple plus 3 bananas plus another banana. It's like you're talking about the same thing. So these things here are called like terms, the 3y and the y. And, basically, like terms are just terms that have the same variable. They both have y to the same exponent or the same power. Right? Not one's not y² or something like that. Okay? So the whole idea is that I can take these things and because they're like terms, I can combine them. So basically, what this expression becomes is it becomes 5 minus x. I can't combine those because they're not similar, but it's like I have 3 bananas and 1 banana, so I can combine that and just say, well, I just have 4 bananas. Alright? That's the whole thing is that you're just going to be combining these like terms. Now let me show you a step by step process for how to do that. Let's just get into our example so I could show you how this works. So we're going to simplify this algebraic expression here. We have 2x plus 3 plus 4 and then parentheses x plus 2. I'm going to simplify this. Remember, that means I want to reduce the number of terms. So the first thing you're going to have to do in this is actually kind of follow some order of operations. I see this 4 that's on the outside of a parenthesis. So the first thing you want to do is you want to distribute constants and variables into parentheses, if you have any. You kind of have to, like, expand this expression before you can start collapsing and reducing it, so that's what you have to do first. The 4 distributes into the x and the 2, and it just becomes 4x+8. We've seen that before, and I'll just rewrite the other terms over here. This is 2x. Alright. So now what I what I can see here is I have a term that has a 2x and a term that has a 4x, and then I have a term that was just a 3 and an 8. So I've got some stuff that is variables and some things that are numbers here. Alright? So that brings us to the second step. So we already distributed. The second step is you're going to group together the like terms, and the way you group them together is you just write them next to each other. So what do I mean by this? I want to basically write the 2x and the 4x so that they're side by side. So what I have to do is I have to get the 2x and I have to bring over the 4x, but I have to bring over the sign that's in front. So in other words, I have to bring over the 4x to bring that whole thing over and make sure that I'm keeping my signs correct. So then I have a plus 3, and then I have a plus 8 over here. Alright. So you're kind of just picking up these terms and repositioning them, and you can do that because everything's added here. Alright. So that's done. So notice how we have now the terms that are similar to each other next to each other. So that's grouping. Now that brings us to the last step, which is just combining like terms. And the way we combine like terms is just by adding and subtracting. It's kinda like what we did up here. We add 3 bananas and 1 banana into 4 bananas. Now we just do the same exact thing. Right? So I could basically just say that this 2x and this 4x is like 2 apples and 4 apples. This basically just condenses down to 6x. Right? Something like that. So that's the idea here. So I can combine those like terms. This becomes 6x, and I can combine the 3 and the 8 because those are just numbers, and this ends up being 6x + 11. And that's as far as I can go. I can't add 6x and 11 because they're not like terms. It's like I'm adding 6 apples to something that isn't an apple. So that is as far as you can go, and this is your simplified expression. This is how I take something that's 4 terms with parentheses and stuff like that, and we'll see that this actually just simplifies to a very simple expression with 2 terms. That's the whole thing, guys. So let me know if you have any questions, and I'll see you in the next video.
Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Algebraic Expressions
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