In Exercises 97–102, write each algebraic expression without pare...

Question

In Exercises 97–102, write each algebraic expression without parentheses. 1/3(3x)+[(4y)+(−4y)]

Accepted Answer

Welcome back. I'm so glad you're here. This is to write down the following expression after removing the brackets. Essentially they want us to simplify. So let's rewrite this. We've got brackets, parentheses two X squared plus for X parentheses minus new parentheses, three x minus X squared and parentheses and brackets and new parentheses. This is all times one divided by X. All right. So what do we do first? Well, we recall from previous lessons that we have an acronym Pem Da's to help us remember the order of operations. And that means that we're going to start with parentheses than work with exponents then multiplication and division from left to right and then addition and subtraction from left to right. I want to note a couple of things. We've got different types of parentheses here. These are the regular parentheses and brackets also function as parentheses in the order of operations. So we always start with the inner most parentheses. Which ones are the innermost parentheses? Well we've got two that are on the inside and let's just start on the left. We've got two X squared plus four X. And for parentheses we ask ourselves what operations going on inside there. Well we've got addition but there is one snag with addition and subtraction and that is that you can only add and subtract like terms and two X squared plus four X will those Xs have different degrees and we cannot add them. So addition is not the purpose of those parentheses. So now we look and say are these parentheses indicating multiplication because that can happen quite a bit where you've got something squished up right in front of the parentheses And it's supposed to be distributed to what's inside. But this time there isn't so really we can just go ahead and drop those parentheses. So this can just come down to X squared plus four X. Now let's take a look at the second set of parentheses here. We have a three x minus X squared. Well that's subtraction. Are they like terms, nope, they've got different degrees. We cannot subtract those two terms. So are these parentheses functioning like multiplication? Is there something squished up in front of them? And yeah, there's this subtraction sign meaning there's an invisible one here. That means a negative one has to be distributed to the two terms inside here so that we know to subtract both of those terms. So we can distribute the negative one negative one times three X negative three X negative one times negative X squared is positive X squared. And that drops off that second set of parentheses. Bring everything else down. And now we are still with the p independence because we've got these brackets here which function like parentheses and what operations are going inside of our brackets. We've got addition. We've got subtraction and we've got addition. There's no exponents multiplication or division. We're just on that addition and subtraction step within our parentheses. So we can go ahead and say are there any like terms that we can add and subtract. Well we've got this two X squared plus this X squared here and then we've also got a four x minus a three X. That we can combine. So combining the two X squared plus X squared, gives us three X squared. And then combining the plus four X minus three X, gives us a plus X. And then we can bring down this times one divided by X. Great. We've still got that parentheses here and we know that those aren't like terms inside three X can't be added to X. So we can't do the addition. Is there something that it's being multiplied by? That needs to be distributed? Yes, we've got multiplication here. This one over X has to be distributed to the two terms inside. So let's go ahead and do that. We've got three X squared times one over X plus X times one over X. And now we can do some simplification. See what cancels out this X in the denominator will cancel out one of the X. Is so I'll just cross off that exponents. So it'll just be three X. And over here this X in the numerator will cancel out the X. In the denominator. Those are all ones. And so now we can multiply straight across three X times one. Well that is three X plus one times one. That is one. Those two aren't like terms we can't do any more addition here. So we look at our answer choices and this matches with answer choice. D. Well done, we'll catch you on the next one.

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