/*! 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 57 Factor using the formula for the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 57

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

Short Answer

Expert verified
The factored form of \(x^{3}+27\) is \((x+3)\) times \((x^{2}-3x+9)\).

Step by step solution

01

Identifying Cubes

To begin, identify the terms that can be expressed as cubes, i.e., the cube roots. In this expression, x^{3} can be written as (x)^{3} and 27 as (3)^{3}.
02

Apply the Sum of Cubes Formula

Apply the sum of cubes formula, which is \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}). Hence, replace 'a' with 'x' and 'b' with '3'.
03

Final Expression

Substitute the values of 'a' and 'b' in the formula (x+3)(x^{2}-3x+9)

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

$$\text { Factor completely.}$$ $$y^{7}+y$$

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{7(x-3)}{2 x-16}, \text { for } x=9$$

Factor and simplify each algebraic expression. $$\left(x^{2}+3\right)^{-\frac{2}{3}}+\left(x^{2}+3\right)^{-\frac{5}{3}}$$

$$\text { Factor completely.}$$ $$(x-y)^{4}-4(x-y)^{2}$$

Find the union of the sets. $$\\{1,2,3,4\\} \cup\\{2,4,5\\}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

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.