/*! 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 60 \((5-8 k)-\left(k+3 k^{2}\right)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 60

\((5-8 k)-\left(k+3 k^{2}\right)-\left(4 k^{2}+1\right)\)

Short Answer

Expert verified
4 - 9k - 7k^2

Step by step solution

01

- Distribute the Negative Signs

Rewrite the expression and distribute the negative signs across the parentheses: (5 - 8k) - (k + 3k^2) - (4k^2 + 1) = 5 - 8k - k - 3k^2 - 4k^2 - 1
02

- Combine Like Terms

Group and combine the like terms together: For constants: 5 - 1 For single k terms: -8k - k For k虏 terms: -3k虏 - 4k虏
03

- Simplify Each Group

Simplify each group of like terms: Constants: 5 - 1 = 4 Single k terms: -8k - k = -9k k虏 terms: -3k^2 - 4k^2 = -7k^2
04

- Combine the Simplified Terms

Combine all the simplified groups together to get the final simplified expression: 4 - 9k - 7k^2

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.

Distributing Negative Signs
First, you need to distribute the negative signs across the parentheses. This might seem tricky at first, but it's just like multiplying a negative number by each term inside the parentheses. Let鈥檚 break it down with an example.

Imagine you have the expression \( (5-8k)-(k+3k^{2})-(4k^{2}+1) \). To simplify it, distribute the negative signs to each term inside the parentheses:

\ 5 - 8k - k - 3k^{2} - 4k^{2} - 1 \

This step is crucial. It sets the stage for combining like terms. Always watch out for negative signs when they appear before parentheses!
Combining Like Terms
Next, you need to combine like terms. What are 'like terms'? These are terms that have the same variables raised to the same power. For instance, \( -8k \) and \(-k\) are like terms because they both have the variable k. Similarly, \( -3k^2 \) and \(-4k^2\) are like terms. Constants like 5 and -1 are also combined because they are simply numbers.

In our example, the simplified expression after distributing the negative signs is:

\5 - 8k - k - 3k^{2} - 4k^{2} - 1\

Let鈥檚 identify and group the like terms together:
  • Constants: 5 and -1
  • k terms: -8k and -k
  • k虏 terms: -3k虏 and -4k虏
Grouping helps to see what you need to simplify or combine next.
Simplifying Algebraic Expressions
The final step is simplifying the grouped terms. Let's go step by step for clarity.

Start with the constants:

\( 5 - 1 = 4 \)

Next, move to the k terms:

\( -8k - k = -9k \)

Finally, combine the k虏 terms:

\( -3k^{2} - 4k^{2} = -7k^{2} \)

Now, you just need to put them all together. Combining all simplified groups, you get the final expression:

\4 - 9k - 7k^{2} \

Breaking it into smaller parts makes the simplification easier to understand. Take it one step at a time, and you鈥檒l master simplifying algebraic expressions!

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

Problem: Simplify: \((5 x-2)(x-3)\) Incorrect Answer: \((5 x-2)(x-3)\) $$ \begin{aligned} &=5 x(x)+5 x(-3)-2 x-2(3) \\ &=5 x^{2}-15 x-2 x-6 \\ &=5 x^{2}-17 x-6 \end{aligned} $$

\(\left(8 x^{3}+14 x^{2}+6 x\right) \div(2 x)\)

The width of a rectangle is \(10 \mathrm{~cm}\) shorter than the length. a. If \(L=\) length, write a polynomial expression in \(L\) that represents the width, and draw a diagram of the rectangle. Do not include the units. b. Write a polynomial expression in \(L\) that represents the perimeter. c. Write a polynomial expression in \(L\) that represents the area.

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

Problem: Simplify: \((2 p-9)\left(3 p^{2}+6 p-5\right)\) Incorrect Answer: $$ \begin{aligned} &(2 p-9)\left(3 p^{2}+6 p-5\right) \\ &=2 p\left(3 p^{2}\right)+2 p(6 p)+2 p(-5)-9\left(3 p^{2}\right)-9(6 p)-9(-5) \\\ &=6 p^{3}+12 p^{2}+10 p-27 p^{2}-54 p+45 \\ &=6 p^{3}-15 p^{2}-44 p+45 \end{aligned} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete 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.