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

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

Algebra

Chapter 1

THE INTEGERS

Section 5

Multiplying Polynomials

The Integers

Equations and Inequalities

Polynomials

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

00:51

Perform the operations and…

03:21

perform the indicated oper…

02:22

Perform the indicated oper…

02:39

03:14

01:00

02:32

02:49

02:11

Simplify.$$\frac{y+\fr…

Hey, everybody, today we'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'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've got that out of the way. We can, uh, start combining like terms. So it'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's going to be negative. Vice Square and the negative and the negative makes a positive. That's what is plus two y and the negative and the positive makes a negative. That's a negative one. So what we'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'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.

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