Problem 77 $8 k\left(2 k^{2}-k+5\right)$... [FREE SOLUTION]

91影视

Elementary Algebra

Laura Bracken, Ed Miller

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 5: Problem 77

$8 k\left(2 k^{2}-k+5\right)$

Short Answer

Expert verified

16k^3 - 8k^2 + 40k

Step by step solution

Distribute the 8k

Apply the distributive property to multiply each term inside the parentheses by 8k. The expression is: \[8k \times (2k^2) + 8k \times (-k) + 8k \times 5\]

Multiply each term

Perform the multiplications: \[8k \times 2k^2 = 16k^3\], \[8k \times -k = -8k^2\], and \[8k \times 5 = 40k\]

Write the final simplified expression

Combine the simplified terms to get the final answer: \[16k^3 - 8k^2 + 40k\]

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.

Polynomial Multiplication

Polynomial multiplication refers to multiplying two or more polynomials together. It involves using distributive property. For example, consider multiplying a polynomial by a monomial, as in the exercise: When multiplying a polynomial like $8k(2k^2 - k + 5)$, distribute the monomial $8k$ to each term inside the parentheses:

Multiply $8k $ by \2k^2\
Multiply $8k $ by \ -k\
Multiply $8k $ by \5\

This systematic distribution allows for more manageable calculations. Hence $8k $ multiplied by each term inside gives: \[8k \cdot 2k^2 + 8k \cdot -k + 8k \cdot 5 = 16k^3 - 8k^2 + 40k\]

Simplifying Expressions

Simplifying expressions involves performing all possible arithmetic operations and combining like terms to reduce the expression to its simplest form. It makes working with complex expressions easier and clear.

To simplify our example:

First, distribute $8k$ to each term inside the parentheses. This removes the parentheses.
Next, carry out the multiplications: \8k \times 2k^2\ becomes \16k^3\, \8k \times -k\ becomes \-8k^2\, and \8k \times 5\ becomes \40k\.
Finally, after performing all multiplications, you combine the results: \16k^3\, \-8k^2\, and \40k\.

This gives the final simplified form: \16k^3 - 8k^2 + 40k\.

Algebraic Expressions

An algebraic expression is composed of variables, coefficients, and constants combined using arithmetic operations such as addition, subtraction, multiplication, and division.

For instance, in the expression $8k(2k^2 - k + 5)$

Importance of Algebraic Expressions

They are fundamental in algebra for representing real-world situations and solving problems. Simplify and manipulate expressions using properties like the distributive property to make solving equations easier and more understandable.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

Distribute the 8k

Multiply each term

Write the final simplified expression

Key Concepts

Polynomial Multiplication

Simplifying Expressions

Algebraic Expressions

Importance of Algebraic Expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Statistics

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.