In Exercises 85–96, simplify each algebraic expression. 18x^2+4−[...

Question

In Exercises 85–96, simplify each algebraic expression. 18x^2+4−[6(x^2−2)+5]

Accepted Answer

Welcome back. I'm so glad you're here. We've got an expression and we get to simplify it. I'll reread it bigger. We've got five minus two X squared plus bracket two times parentheses two X squared minus X. And parentheses plus one and bracket. Now some things that we notice here we have got some terms that aren't like terms that we can't add and subtract together. So it's going to be very important to make sure we're combining like terms when we're doing the addition and subtraction steps and what are the steps? Well we recall from previous lessons that we've got MGa's which reminds us of the order of operations. So we start with parentheses then go through exponents, then multiplication and division from left to right. In addition and subtraction from left to right. But again like I just said we are going to be doing this with like terms when we're doing the addition and subtraction steps. So let's get started. Do we have parentheses? We do we have two sets of parentheses. These regular old parentheses and then we've got brackets which function as parentheses but help differentiate so that instead of just so many parentheses where you can get lost, they alternate parentheses brackets, parentheses brackets. So you can see which ones you're working within. So we always start with the inner most parentheses which is right here, two X squared minus X. So that's a subtraction operation. But we can only subtract like terms are those like terms, nope. They have different degrees. This one's X squared and this one's just an X. There's an invisible one there it's just X. To the first. We cannot subtract those. So we can say that the parentheses have another function here and they do parentheses can often indicate multiplication. So in this case when we have a two squished up against that parentheses then that's going to tell us to distribute the two through multiplication. And is there since we can't do anything in the little parentheses? Is there anything else we need to do in the bigger parentheses? We've got the multiplication going on distributing the two and we've got addition. So looking at our order of operations, parentheses, exponents then multiplication division. So we're going to distribute that to as our first step. So two times two X squared four X squared. We can do multiplication when the terms aren't like terms two times negative X is negative two X. Now we can just bring down the rest. So started with the five minus two X squared plus bracket four X squared minus two X plus one and then end that bracket. Okay we've still got the brackets which are functioning as parentheses here and what can we do within them? Well we've got subtraction and we've got addition but do we have like terms, we do not. We've got an X. Squared and X. And one and we can't combine any of those. So we say is this bracket functioning like multiplication is their number squished up against here. Well there's an invisible one that we could multiply by everything but I mean we don't really have to multiply everything by one. So we can just drop those brackets for our next step. We've got five minus two X squared plus four X squared minus two X plus one. And now we're just looking at let's see we've got parentheses exponents done any other multiplication or division, nope there isn't. So it's just addition and subtraction and just of like terms. So do we have anything that can go with the five? Well the only other like term here with no excess attached to it is the one so five plus one. So we can write that. I'll write that at the end here we've got plus six and we can bring down the rest negative two X squared plus four X squared minus two X. Now any other like terms? Well how about our x squares? We've got negative two X squared plus four X squared. Well that's going to give us two X squared. Now we can bring down the rest two X squared minus two X plus six. Are any of those like terms? Um anything that can be combined there nope none of them are like terms. So that means we've simplified it as much as we possibly could and that matches with answer choice. A well then we'll catch you on the next one

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