/*! 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 62 Factor using the formula for the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 62

Factor using the formula for the sum or difference of two cubes. $$27 x^{3}-1$$

Short Answer

Expert verified
The factored expression of \(27x^{3}-1\) using the formula for the difference of cubes is \((3x - 1)(9x^{2} + 3x + 1)\).

Step by step solution

01

Identifying the values of a and b

The first thing to do is to rewrite the given expression in the form of \(a^3 - b^3\). The equation \(27x^{3}-1\) can be rewritten as \((3x)^{3} - (1)^{3}\). Therefore, we identify \(a = 3x\) and \(b = 1\).
02

Apply the formula

Using the formula of difference of cubes \(a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})\), and inserting the identified values \(a = 3x\) and \(b = 1\), we get: \[(3x - 1)((3x)^{2} + 3x*1 + (1)^{2})]\.
03

Simplify the expressions

Now, simplify the above expression by calculating the square and product terms: \[(3x - 1)(9x^{2} + 3x + 1)\].

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!

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

$$\text { Solve for } C: \quad V=C-\frac{C-S}{L} N$$.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells personalized stationery. The weekly fixed cost is \(\$ 3000\) and it costs \(\$ 3,00\) to produce cach package of stationery. The selling price is \(\$ 5.50\) per package. How many packages of stationery must be produced and sold each week for the company to generate a profit?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$6+\frac{1}{x}=\frac{7}{x}$$

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{4}}=-2$$

Perform the indicated operations. $$\left(1-\frac{1}{x}\right)\left(1-\frac{1}{x+1}\right)\left(1-\frac{1}{x+2}\right)\left(1-\frac{1}{x+3}\right)$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.