Express the following in index form. So the expanded form is this. So when we don’t leave it in index form when I just like spread it all out that’s expanded form. And I want to convert this to index form. All you need to know is how many of each prenumeral or number we have? So here we have a! How many a’s do we have? One two three four, so all we need to write is a to the power of four because there’s four lots of a’s.
That’s all we’re asked to do. So b! you can tell me the answer but it’s a little bit different because we’ve got different prenumerals. And make sure guys, you gather the like terms together. So here! There’s a and b. How many a’s? There’s one two three a’s and b, there’s one two b’s. So it’s going to be a cubed times b squared, okay? Now you can I mean you can write this as a cubed times b squared but you don’t really need the time multiplication sign there because if there’s nothing in between. It simply means multiply so I mean you can write it like that. But it’s probably more simpler to write it like. Probably more simple to write it like this, okay? So this is there what it means. So three lots of a’s two lots of b’s.
C! Okay! So see how we’re doing a times b plus a times b times a. If we have a plus or minus in between. You only look at where it multiplies. Don’t do anything with the addition. So as long as they’re like terms, you can add up but here, I’m just using brackets. Just to divide these up, just you don’t get confused. What’s a times b? a times b is just ab. And here there’s two lots of a’s and one b, so it’s going to be a squared b because there’s two lots of a’s and one b. And we simply add them up but we can’t add them up because they’re not like terms.
So we leave it like that, that’s all we’re asked to do, okay? With the groupings! Now d! Okay so we have minus and a plus, so all you need to try and simplify are these we’re multiplying. So with a times b. We’ve got one a one b, here we’ve got one a and two b’s and here, we’ve got three a’s. So how do we write it? Do you guys want to try?
This is what I’ve got. a times b is just ab. You don’t have to put the multiplication sign there and there’s two lots of b’s here and one a, so it’s just going to be a times b squared or just a b squared plus there’s three lots of a’s, so a cubed, okay? Or a to the power of three. That’s what I have to do it here. So it’s very very simple
The numbers trying to put all the numbers out the front. So see how seven here, we’ve got eight here, and we’ve got four here, just leave them as it is, okay? Because they’re the only numbers in each part. So again I’ll just like kind of group them. Make sure you don’t like, merge them, okay? So keep these in the front keep these in the middle, keep these in the end, don’t try to like merge them together for some reason. You can’t do it because they’re not like terms.
So there’s three lots of a’s, two b’s, two c’s. So the first one will be seven a cubed, the second one will be minus eight b squared, the last one will be four and c squared. a times a plus a times b minus a times a. I’ll just actually show you. You guys should be okay with this now. I’ve got two a’s, got a and b, and we’ve got two a’s. Remember guys I said add your gather your like terms if you do have any. See how a squared and a squared here. They’re like terms. So we can gather them. So what’s a squared minus a squared? Zero!
So we actually eliminate these. So we’re just left with a b, so ab is the answer. Count how many of each in each part and write it like an index form like this, okay? So hopefully I don’t have to explain that again. And you can see here, three a squared and two a squared are like terms. So we actually can group them together. So three a squared plus two a squared is, well a squared is a like term. So you’re going to add up your numbers in front which is going to be five a squared plus the remaining number a squared plus a squared b, okay? That’s pretty much it.
Let’s gather the like terms again. Kind of guys just write these in index form. See there’s two a’s here two a’s here and two a’s here. So you should have 3a squared minus 7a squared plus 2a squared. What can you see guys? They are all like terms because they all end in a squared. So we can gather them all together. So now you just need to worry about the numbers. What’s three minus seven plus two? Three minus seven plus two is minus two. So or negative two. Negative two a squared
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