/*! 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 91 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 91

Simplify each expression. $$ 8-7\left(k^{3}+3\right)-4 $$

Short Answer

Expert verified
-7k^3 - 17

Step by step solution

01

- Distribute the -7

Apply the distributive property to \begin{enumerate}\tem \t-7(k^{3} + 3)een distributing the \tem -7en across each term inside the parenthesis:\[-7(k^{3} + 3) = -7k^{3} - 21\]so the expression becomes:\[8 - 7k^{3} - 21 - 4\].
02

- Combine Like Terms

Combine constants in the expression. Performing the arithmetic on the constants:\[8 - 21 - 4 = -17\]So the simplified form of the expression is:\[ -7k^{3} - 17\]

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.

Distributive Property
The distributive property is a useful tool in algebra that helps in breaking down complex expressions. It involves distributing a single term across the terms inside parentheses. For example, if you have -7(k^3 + 3), you need to multiply -7 by each term inside the parentheses.
Here's how it works: multiply -7 by k^3 to get -7k^3, and then multiply -7 by 3 to get -21.
So, -7(k^3 + 3) becomes -7k^3 - 21. This makes the expression much simpler to work with and leads to a more manageable equation.
Combining Like Terms
Once you've used the distributive property, the next step is to combine like terms. Like terms are terms that have the same variable raised to the same power. In the given example, the constants are 8, -21, and -4.
To combine like terms:
  • Add or subtract the constants: 8 - 21 - 4 = -17.
  • Make sure you only combine terms that are exactly alike in terms of variables and their exponents.
By combining constants, the expression simplifies further to: -7k^3 - 17. This reduction is crucial for the final and simplest form of the equation.
Algebraic Simplification
Algebraic simplification is the process of making an algebraic expression as simple as possible. After using the distributive property and combining like terms, the resulting expression is the simplest form it can be.
For the original problem, after distributing -7 and combining the constants, we found that 8 - 7(k^3 + 3) - 4 simplifies to -7k^3 - 17. This is the most simplified form of the expression.
Simplification helps in understanding and solving equations more easily. It involves:
  • Removing parentheses using the distributive property.
  • Combining like terms.
  • Ensuring the expression is in its simplest possible form.
A well-simplified expression is easier to interpret and work with, making it an essential skill in solving algebraic problems.

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

Find each product or quotient. $$ 9\left(\frac{2 y}{9}\right) $$

Find each product or quotient. $$ \frac{-8 x^{2}}{4} $$

Simplify each expression. $$ (2 x+3)+(7 x+5) $$

Use an operation with signed numbers to solve each problem and identify the operation used. Explain why 0 is the only real number that does not have a multiplicative inverse.

Simplify each expression. $$ 5 w-2+4(w-3)-6(w-1) $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.