/*! 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 46 In the following exercises, subt... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 46

In the following exercises, subtract the polynomials. \(\left(10 r^{2}-20 r\right)-(r-8)\)

Short Answer

Expert verified
The result is \( 10r^{2} - 21r + 8 \).

Step by step solution

01

Distribute the Negative Sign

When subtracting polynomials, distribute the negative sign across each term in the second polynomial. In this case, distribute the negative sign to each term in \( (r - 8) \): \( -(r - 8) = -r + 8 \).
02

Rewrite the Expression

Rewrite the original expression with the distributed negative sign: \( 10r^{2} - 20r - (r - 8) = 10r^{2} - 20r - r + 8 \).
03

Combine Like Terms

Combine the like terms: \( 10r^{2} - 20r - r + 8 = 10r^{2} - 21r + 8 \).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combine Like Terms
The final step in subtracting polynomials is to combine like terms. Like terms are terms that have the same variable raised to the same power. In our problem, we have:
\begin{align*} \left(10 r^{2}-20 r - r + 8 \right) \end{align*}\br>Combine \( r \) terms:
\[ -20r - r = -21r \]
Now the expression becomes:
\[ 10r^2 - 21r + 8 \].
So, we end up with the final simplified expression:
\[ 10r^2 - 21r + 8 \].
By following these steps, you ensure a systematic approach to subtracting polynomials. Remembering to distribute the negative sign, rewrite the expression, and combine like terms will make the process straightforward.

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

Multiply the binomials. Use any method. $$ \left(x^{2}+3\right)(x+2) $$

Find each product. $$ \left(2 x^{2}-3 y^{4}\right)\left(2 x^{2}+3 y^{4}\right) $$

Find each product. $$ (s-7)(s+9) $$

Multiply using (a) the Distributive Property; (b) the Vertical Method. $$ (x+5)\left(x^{2}+4 x+3\right) $$

Square each binomial using the Binomial Squares Pattern. $$ (3 x-y)^{2} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

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.