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Reading Blueprints. Find a polynomial that representsa. the difference in the length and width of the one-bedroom apartment.b. the perimeter of the apartment.

$x^{2}+a x$

Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

Polynomials

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:09

a. What is the difference …

00:40

Find a polynomial that rep…

00:35

00:14

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00:26

Find a polynomial for the …

02:02

Find $(a)$ a polynomial th…

02:22

02:30

02:17

00:56

00:41

01:01

00:34

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00:32

01:55

So in this problem, we're given the blueprint of a house, which I droop a little bit off onto the right. I didn't put in all of the different rooms. I only put in the bedroom because reading the problem, that's the only specific room that we're going to be talking about. But I didn't put in all of the other measurements. So in part A, they're being asked to find the difference in the length versus the with off that one bedroom. Remember, difference means subtraction, so they want us to subtract the length fromthe with. So if we want to find the difference in the length in the length in the with. So in our bedroom, the length of it is for explosive tree, and the whiff of the bedroom is X squared minus six x plus tree. So if we want to find a difference between the length and the width, we simply need to subtract. Um, well are with is the quantity X squared minus six X plus three minus the length, which is four X plus three. Well, essentially, we just subtracting Paulino meals, so the terms in the first polynomial will just get brought down, so we'll have X squared minus six X plus three. And for the second polynomial, we simply need to change their signs. So the positive for X becomes negative for X and the positive three becomes negative three. And now we simply need to combine like terms. Well, you know this. The X Square does not have a late term so that we'll get brought down. Negative six x has a late term negative for ex Well, negative six x minus four X is negative 10 x and positive. Three has a late term in negative three. But those air gonna cancel each other out. So what we find is the difference between the length and the width is the quantity X squared minus 10 X Because our problem gives us units, we should use those in our final answer. So she also mentioned that it's a difference in feet now for part B. We're being asked to find the perimeter off the entire apartment. Well, to find perimeter, we essentially just need to add up all the side lips. Well, because it's a rectangle. The with is going to be this beat the same on both sides and the length will also be the same on both sides. So for part B to find the perimeter, essentially, we can do two times what we would get when we do the with, plus two times the length well, To find the whiff, we need to add three X plus one an X squared minus six X plus three. So we're gonna do two times the quantity of three X plus one, plus the quantity of X squared minus six X plus three. And then we're gonna add this to two times are length well, our length. We need to add X squared minus X plus six plus for explosive tree. So we'll have plus two times the quantity of X squared minus X plus six, plus the quantity of four X plus three. So now, looking within that first set of parentheses because we're adding, we simply need to combine like terms, so we will be left with two times the quantity off. Now let's find our light terms. Let's start with our ex Greater. It doesn't have a late term, so we just need to bring it down. Our next term is three bucks. Which life term is negative. Six X Well, three months. Six is negative. Three. So we'll have negative three X and then lastly, we have positive. One who's like term is positive three. So we'll get positive for now. We'll do the same thing for our life. We're gonna have plus two times. So again, we're gonna find our like terms. Well, X Square does not have a life term, so we'll have X squared are negative. X has a late term of positive for ex. Well, negative one plus fours. Positive three. So what? Positive Three X and six has a late term of three, while six plus three is not. So what? Positive night. So now I'm going to go on to a different screen just because I'm running out of room. So we're gonna have two times the quantity and I'm gonna keep scrolling back so I can remember it. We have X squared minus tree experts for plus two times are length, which we found to be X squared plus three X plus nine. And now we need to simplify this discretion. Well, first, we need to distribute the to teach term in both sets of prophecies, so I'm gonna multiply each of these terms by two. Well, two times X squared is two ex word. Two times negative. Three exes, negative six x and two times four is positive. A. I nail need to do the same thing for my second Senate prep. See, I need to distribute the two to each of those terms. Well, two times X squared is positive to X square two times three x is positive. Six x and two times nine is 18. And now we just need to combine our life terms. So let's start with two ex work. Well, it's like term is also to X word. Well, two plus two is four, so we'll be left with four x squared. Our next term is negative. Six. X Who's like term is positive? Six. Sex while negative six plus 60 So those terms will cancel each other row. Next, we have positive. Eight. Who's like charm is positive. 18. Well, eight plus 18 is 26. What? Plus 26. So now we've found an expression to represent the perimeter of the apartment. And because we're giving units, we should also give units in our answer, which in this case will be feet. So what we've found is DEA permit There would be for X squared 26 feet

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