/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 Find each product. In each case,... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 69

Find each product. In each case, neither factor is a monomial. $$(y-3)\left(y^{2}-3 y+4\right)$$

Short Answer

Expert verified
The product of \( (y-3) \left(y^{2}-3 y+4\right) \) is \( y^{3} - 6y^{2} + 13y - 12 \).

Step by step solution

01

Expand the Expression

The first set of terms is \( (y-3) \) and the second set of terms is \( \left(y^{2}-3 y+4\right) \). To solve this, each term in the first set of parenthesis should be multiplied by each term in the second set, resulting in: \( y(y^{2}-3 y+4) - 3(y^{2}-3 y+4) \).
02

Distribute the Terms

Multiply \( y \) through \( y^{2}-3 y+4 \) and \( 3 \) through the same set. This gives us: \( y^{3} - 3y^{2} + 4y - 3y^{2} + 9y - 12 \).
03

Combine Like Terms

Combine the terms that have the same powers of \( y \). Identifying these and combining them gives us a result of \( y^{3} - 6y^{2} + 13y - 12 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What polynomial, when divided by \(3 x^{2}\), yields the trinomial \(6 x^{6}-9 x^{4}+12 x^{2}\) as a quotient?

In Exercises \(79-82,\) simplify each expression. $$\frac{6 x^{3}(3 x-1)+5 x^{2}(6 x-3)}{3 x^{2}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. It is not possible to write a binomial with degree \(0 .\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$

Use the motion formula \(d=r t,\) distance equals rate times time, and the fact that light travels at the rate of \(1.86 \times 10^{5}\) miles per second, to solve. If the moon is approximately \(2.325 \times 10^{5}\) miles from Earth, how many seconds does it take moonlight to reach Earth?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.