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Question

Perform the indicated operations and write the result in simplest form.
$(y-1)\left(y^{2}-2 y+1\right)$

Aditya Sood · Accepted Answer

Hey, everybody, today we&#x27;re going to be solving problems. 17 uh, performed the indicated operations and write the result in simplest form. Why minus one times y squared, minus two y plus one. So we&#x27;re going to expand this and the easiest way to expand this is going to be to multiply. Why, with all of these terms, as the arrows indicate, and one with all of these terms, as the arrows indicate. So when you want to play, why, with all off the terms and this expression we get, why times y squared, Which is why cubed. Why times that of two. Why? Which is number two s squared and white times one, which is why then this negative sign will carry over right over here. And we can multiply one with all of these expressions. So one time. So I squared. Well, give us y squared one times dagger to why will give us never left a wife, and one times one will also give us one. So now that factoring has gotten, we&#x27;ve got that out of the way. We can, uh, start combining like terms. So it&#x27;s going to be why cubed minus two y squared plus why and then this negative sign here. This is tricky. We want to distribute that into this expression, so it&#x27;s going to be negative. Vice Square and the negative and the negative makes a positive. That&#x27;s what is plus two y and the negative and the positive makes a negative. That&#x27;s a negative one. So what we&#x27;re left with is why cubed minus two y squared plus why minus y squared plus two wide minus one. And that was just a matter of combining our light terms. So it&#x27;s why cubed and this negative to y squared gets together with this negative y squared to get negative. Three. Why Square, Um, why plus two? Why is three wife and everyone? So our answer is why cubed minus three y squared plus three y minus one.

Matt Gibson · Answer

our first step is to distribute. I like to put a little one here and here. Ah, and here and here to remember I am going to be adding my exponents here. So this becomes why Cuba Can I add my exponents minus Why minus Why Cuba can I add my exponents there minus? Be careful with distributing that negative minus two y squared minus two y squared again It&#x27;s one plus when I had my exponents Plus two Why combine your leg terms? This is one minus one gives me Know why Cubes my wife squared. I have a negative to in a negative to give me a negative four. My exponents stays the same. And then finally a negative one y plus two. Why gives me a positive one? So it is right. Plus why?

Anna Myers · Answer

Okay, so this problem we want to simplify. Why? To the negative one minus y close to to the negative one all over to. And remember that if you have a to the negative end, it&#x27;s the same as one over aid to the end. So if you move the number raised to the exponents into the denominator become makes the exponent positive. So we can do that with what we have. We can move it to the denominator. So we would then have one over why, minus one over Why Plus two, You have to put the exponent race to the first power because it&#x27;s just itself all over two. So in order to subtract the need to have the same denominator, so this needs to be multiplied to that one, and that one needs to be multiplied by that one. So we have one over. Why multiplied by Y plus two over y plus two. Make sure you do it both to the top and the bottom minus one over y plus two times y over. Why and then that&#x27;s all over two so that when you rewrite it, you&#x27;ll have y plus two all over. Why tell me. Why? Blessed to minus Why who are y times y plus two all over to. And then now you can combine them and subtract. Since you&#x27;ve got the same denominator, do you have y plus two minus y? So those will cancel out over Why times why I plus two all over to so two over Why? Why? Plus two. And then remember, when you have when you have something like this being divided, buy something else. Another denominator. You can divide it by just flipping the reciprocal flipping the number so the two would go to one half and multiplying at times that so you would do to over why times worthless sue times one half. So it&#x27;s flipped down onto the bottom. Those would cancel out, and then it would leave you with one over. Why times y plus two. So that would be your answer. There you go. Remember, you don&#x27;t want your denominator to ever equal zero. So in this case, why I cannot equal zero or negative too. There you go.

Alekhya Bhupalam · Answer

So in this problem, we&#x27;re trying to simplify one minus two. Why squared so right away? This is different than most of the other problems that have been given. But then again, we know is squared. So this tells us this is nothing but one minus two y times one minus two y. This looks more familiar because it&#x27;s a polynomial times a polynomial. And what what were used? Thio And since, um, this is basically just squared. So it&#x27;s just we&#x27;re multiplying the polynomial by itself twice. So this is a more familiar format, and from here we can then think of the acronym foil and apply that to when we are distributing out and multiplying out the two polynomial school. So first we have f, which means we multiply out the first terms. So first term Zehr one and one, So that is going to give us one simply one. Next we have the which is the outer terms. So that&#x27;s gonna be one and minus two y. So one minus two wise nothing but minus two. Next, we have the inner terms, so that is minus two y and one which is nothing but minus two y again. And lastly, we have the last terms. The last terms are minus two I and minus two I. So we have negative two I times negative to I that is going to give us plus four y Square because we multiplied them together. So it&#x27;s plus four y squared. So finally, we have to rearrange this so we should have the y squared term at the front because that&#x27;s our highest number of terms. We&#x27;re gonna move the four wide square to the front. Next, we&#x27;re going to have a wise terms because they are second greatest term here. So we also have to combine the like terms here that&#x27;s going to give us minus two. I, um, negative to I managed to eyes nothing, but minus four. Right? So it&#x27;s just simply minus four right here and then, Lastly, we have just a constant, which is gonna be at the end. And that&#x27;s gonna be plus one. So our final answer here is four y squared minus four y plus one

Ankit Gupta · Answer

in discussion. We have to simplified are given explosion right less One do I did by lying minus new a minus bi minus one. Yeah, I did buy y minus four. Now it combined the reflections Life I linger on one. Your nominator That is white. This one You. I did by y minus True market Rabbi rule divided by U minus Y minus one. You already but white minus four. So on simply Vanga First election. Bigger room. I did not write this one. You write it by no light minus four. Minus my minus one. Divided right by minus. Or now, on combining the university does bigot y last three You are did by why u minus

Brandon Fox · Answer

to start this problem, we&#x27;re gonna take the Y plus one and distributed into the other polynomial toe every term. So let&#x27;s start with y squared. Here we got why squared times the Y plus one and then the minus y times the Y plus one and then the plus one times the Y plus one. And this is the whole left side here minus this minus sign right here and then let&#x27;s do the other side. So let&#x27;s distribute this mine it Why, minus one into every term of this polynomial. So let&#x27;s start with a Y Square. So why squared times y minus one plus why times why minus one and then a plus one times why minus one And this is the whole right side. Let&#x27;s do some distribution through the whole thing. So why squared times? Why is why to the third power in why square times one is a plus y squared a minus y times. Why is a minus y squared in a minus? Y times of one is a minus y One times Why is a plus? Why and one times one is plus one. So this is now my whole left side unless attract the right side over here. Why? Square times Why is why cute and why squared minus one is a minus y squared. Why times why is a plus y squared in white times? A minus one is a minus. Why, one times why is a plus why? And one times one is a minus one. So let&#x27;s combine some light terms. Um, so why cute is here? And we have let me move this actually down a little bit. But I think some things were gonna cancel if I noticed the Y squared plus y squared in a minus y squared are gonna cancel in a minus Y an a plus, we&#x27;re gonna cancel. So all they really have left is the why queued plus one on the side, minus on the other side, in the same thing here, this minus y squared. And this plus y squared are going to cancel, and the minus y in the plus, we&#x27;re gonna cancel. So I just have the y cube in the minus one. So analysis attract here in the middle these like terms. Why cubed minus y cubed. They&#x27;re gonna cancel, make zero and then one minus a negative one. This is actually to the answer, then is to

Problem

Perform the indicated operations and write the re…

Problem 17 Hard Difficulty

Perform the indicated operations and write the result in simplest form.
$(y-1)\left(y^{2}-2 y+1\right)$

Answer

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

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Ann Xavier Gantert

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Absolute Value - Example 1

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

Algebra 2 and Trigonometry

Heather Z.

Kayleah T.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Heather Z.

Kayleah T.

Maria G.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry