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

$$3 x+1$$

Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

Polynomials

Campbell University

Harvey Mudd College

Lectures

01:24

Perform the indicated oper…

01:51

Perform the operations.

02:27

02:09

02:43

00:40

Perform the operations and…

00:58

02:25

01:48

01:35

01:47

01:52

00:30

Perform each indicated ope…

02:15

01:05

01:19

01:43

03:22

02:16

we're being asked to perform the given operation. Well, if you know this in this problem, we have three different sets. Appalling wheels. So less first, just focus in on the 1st 2 So I'll separate those by putting a bracket around our 1st 2 Paulino meals. So for these two pollen, no meals were being asked us. Attract them. And we know that because there's a minus sign in between. The two sets of embassies will remember to subtract Paulino meals for this first set. You just need to bring down those terms so we can just bring down to X squared minus three x plus one. However, for the polynomial that's getting subtracted by the original meaning the second Prem facie, we simply need to change all of the signs for each term within that prophecy. And then we can get rid of our parentheses. So, for example, that positive for X squared becomes negative for X, where the negative three x becomes positive three x and the positive to becomes negative too. Now we simply need to combine like terms. Well, two x squared. It's like term is negative for ex worth, while to X squared minus four X squared is negative to export. So we have negative two X squared. Our next late term is negative. Three acts Well, that has, upon a like term, a positive three ex well, negative three plus 30 So those terms will actually cancel each other out. And lastly, we have one minus two, while one minus two is negative. One so minus one. Now I'm going to bring down my next polynomial, which I could have written in my second line as I should have. But it just goes to show that pony no meal is just being brought down each time. Now we're being asked to add to Paulina meals because in between, both sets of prep sees we have a plus sign will remember toe add Paulino meals. We can use the community of an associative properties to regroup and reorder our like terms. So let's start with our first term negative two X squared. It's like term is positive two X squared so we can put those together as negative two X squared, plus positive to X ray. Well, our next term is negative one. It's life term is positive, too, so we can group those together as the quantity of negative one plus two. And if you know this, our last term is just positive to react, so we can just bring that down in the yet Now we just simply need to combine our like terms. Well, negative two X squared plus two X squared is going to be zero because negative two plus two is equal to zero. So those actually cancel each other out. If you look at our next set of prophecies, we have negative one plus two, which is positive one. Then remember, three ex did not have a late term, so that can just be brought down as positive three x So our final answer is one plus three x.

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00:17

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00:53

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00:39

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01:12

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00:35

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