Problem

Perform the operations. $$ \begin{aligned} &4 x^{…

00:54

Problem 100 Hard Difficulty

Perform the operations.
$$
\left(-3 z^{2}-4 z+7\right)+\left(2 z^{2}+2 z-1\right)-\left(2 z^{2}-3 z+7\right)
$$

Answer

$-3 z^{2}+z-1$

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Algebra

Elementary and Intermediate Algebra 5th

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

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Video Transcript

we're being asked to perform to given operations off. You know this in this problem, we're given three different Paulino meals. So what we can do first is just concentrate on the 1st 2 polynomial, so I'm going to put a set of brackets around them. Well, we're being asked to add the two Paulino meals. So using the community and associate properties, we can regroup our terms. So that way we can have real, like, terms together. So I'll start with the first time we have negative three z squared, and it's like term would be to Z squared. So I'm gonna bring down my brackets and I'm gonna group those two terms together. So we'll have negative three z squared plus two z squared. Well, our next term is negative for C. Well, it's like term is positive. Choosy. So weaken group those terms together as well. So we'll have plus the quantity of negative for Z Plus two Z. Now our next term is positive. Seven. Well, it's like term is negative one, so we could group those together as well, So we'll have, plus the quantity of seven minus one. That's a seven there. And then I'll put my bracket and all I'm going to do is bring down my last polynomial for right now. So we'll have minus two quantity of two Z to the second, minus three Z plus seven. Now we can go ahead and combine those like terms. Well, negative three z squared, plus two Z square. Well, negative. Three plus two is negative one. So what? Negative one C square. In our second set of prophecies, we have negative for C plus two z. All negative. Four plus two is negative too. So I'm negative, too. See? And there are less other prophecies. We have seven minus one, which is six swept plus six. And again, just like I said before, we're gonna bring down that last polynomial. So minus the quantity of two Z square minus three C plus seven. Now, if you know this, we're now just left with the subtraction to Polly. No meals. So to do this, what we're gonna do first is we're gonna bring down our terms in the first polynomial. So negative one z square minus juicy plus six. And remember, in our second Paulino meal, which is the one getting subtracted by the first, we simply need to change each of the signs for each of the terms. And then we can drop our parentheses. So, in other words, that positive to Z squared is going to come negative to C squared, the negative three z will become positive three z and the positive seven will become negative seven. And now we just need to combine like terms. So start with our first term negative one c squared. Well, it's like term is negative. Choosy square. Well, negative one minus two is negative. Three. So what? Negative three C square. Our next like term is negative. Choosy? Well, negative twosies late term is positive. Three z Well, negative two plus three is positive one. So it plus one z In our last terms, we have post six minus seven. Well, six minus seven is negative one, so we can lead this as our final answer. However, if you take a look at that middle term, we have a coefficient about one there which we don't actually have to write. So we could also say that our final answer is negative. Three c squared plus Z minus one

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