/*! 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 10 \(\left(24 c^{3}-8 c\right) \div... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 10

\(\left(24 c^{3}-8 c\right) \div(8 c)\)

Short Answer

Expert verified
3c^2 - 1

Step by step solution

01

Identify the Expression

First, identify the given expression: (24c^3 - 8c) / (8c)
02

Distribute the Denominator

Distribute the denominator, 8c, to each term in the numerator: (24c^3) / (8c) - (8c) / (8c)
03

Simplify Each Term

Simplify each separate fraction: (24c^3) / (8c) = 3c^2 (8c) / (8c) = 1
04

Combine the Results

Combine the simplified terms to get the final answer: 3c^2 - 1

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.

Simplifying Expressions
Simplifying algebraic expressions is a fundamental skill in algebra. This process involves reducing the expression to its simplest form by performing basic arithmetic operations and applying algebraic rules.
To simplify the expression \((24c^3 - 8c) / (8c)\), follow these steps:
  • Identify each term in the numerator.
  • Distribute the denominator to each term in the numerator separately.
  • Reduce the fractions by canceling out common factors.
  • Combine the simplified terms to get the final result.
In this example, we separated the original expression into two simpler expressions, \(\frac{24c^3}{8c}\) and \(\frac{8c}{8c}\), and then simplified each independently. This step-by-step approach makes complex expressions more manageable.
Fraction Distribution
Fraction distribution involves spreading a single denominator across multiple terms in the numerator. This makes it easier to simplify each term separately. Here's the process using our example:
  • Start with the expression: \((24c^3 - 8c) / (8c)\).
  • Distribute the denominator \(8c\) to each term in the numerator: \((24c^3)/(8c) - (8c)/(8c)\).
  • By doing this, we create separate fractions that can be simplified individually.
Distributing the denominator helps in breaking down complex fractions into smaller, simpler parts that are easier to handle. For our example, it makes it clear which parts of the expression we need to simplify next.
Algebraic Fractions
Understanding algebraic fractions is key in algebra. These fractions have variables in the numerator, the denominator, or both. Here's a breakdown using our example:
  • An algebraic fraction like \((24c^3 - 8c) / (8c)\) involves terms with variables.
  • To simplify, we distributed the denominator \(8c\) to each term in the numerator.
  • We then simplified each fraction: \((24c^3) / (8c) = 3c^2\) and \(8c / 8c = 1\).
Combining these results, we get \(3c^2 - 1\).
For any algebraic fraction, always distribute the denominator first, simplify each fraction, then combine the simplified results. Practice makes this process much easier to handle, helping you with more complex algebraic problems in the future.

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

\(\left(2 x^{2}-11 x-21\right) \div(x-7)\)

\(\left(x^{2}+13 x+18\right) \div(x-3)\)

\((3 x-7)(3 x+7)\)

The length of one side of a triangle is \(a \mathrm{ft}\). The other sides of the triangle are \(4 \mathrm{ft}\) longer and \(3 \mathrm{ft}\) shorter than this side. a. If \(a=\) length of one side, write polynomial expressions in \(a\) that represent the lengths of the other sides, and draw a diagram of the triangle. Do not include the units. b. Write a polynomial expression in \(a\) that represents the perimeter.

A customer borrows \(\$ 8500\) for 6 years at a simple interest rate of \(11.3 \%\). Find the simple interest.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Geometry

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.