/*! 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 19 Add or subtract as indicated. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 19

Add or subtract as indicated. $$\left(x^{3}-y^{3}\right)-\left(-4 x^{3}-x^{2} y+x y^{2}+3 y^{3}\right)$$

Short Answer

Expert verified
The final simplified expression is \(5x^{3}+x^{2} y-x y^{2}-4y^{3}\).

Step by step solution

01

Manage the signs

In this step, subtract the second set of terms from the first. This is done by changing the sign of each term in the second parentheses and then adding it to the first:\(x^{3}-y^{3}-(-4 x^{3}-x^{2} y+x y^{2}+3 y^{3})\)Which simplifies to:\(x^{3}-y^{3}+4 x^{3}+x^{2} y-x y^{2}-3 y^{3}\)
02

Combine like terms

Combine terms with the same variable and exponent. There are two \(x^{3}\) terms: \(x^{3}\) and \(4x^{3}\). Adding these gives \(5x^{3}\). There are two \(y^{3}\) terms: \(-y^{3}\) and \(-3y^{3}\). Adding these gives \(-4y^{3}\). The \(x^{2} y\) and \(-x y^{2}\) terms do not have any like terms, so they remain as is. This gives the final expression:\(5x^{3}+x^{2} y-x y^{2}-4y^{3}\)

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?

We have seen that in \(2009,\) the United States government spent more than it had collected in taxes, resulting in a budget deficit of \(\$ 1.35\) trillion. a. Express 1.35 trillion in scientific notation. b. A trip around the world at the Equator is approximately \(25,000\) miles. Express this number in scientific notation. c. Use your scientific notation answers from parts (a) and (b) to answer this question: How many times can you circle the world at the Equator by traveling 1.35 trillion miles?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)-(y-1)\left(y^{2}+y+1\right)$$

Use a vertical format to find each product. $$\begin{array}{r}7 x^{3}-5 x^{2}+6 x \\\3 x^{2}-4 x \\\\\hline\end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.