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Chapter 0: Problem 57

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

Short Answer

Expert verified
\((x + 3)(x^{2} - 3x + 9)\)

Step by step solution

01

Identify the Cubes

First, identify the values that can be represented as a cube. In the provided expression, \(x^{3}+27\), \(x^{3} = a^{3}\) and \(27 = b^{3}\). Thus, \(a = x\) and \(b = 3\).
02

Apply the Sum of Cubes Formula

The formula for sum of two cubes is \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})\). Substitute \(a = x\) and \(b = 3\) into the formula and simplify the result.
03

Substitute and Simplify

Substitute \(a = x\) and \(b = 3\) into the sum of cubes formula to get \((x + 3)(x^{2} - 3x + 9)\). This is a simplified factored form of \(x^{3}+27\).

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Most popular questions from this chapter

What is a linear equation in one variable? Give an example of this type of equation.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two tax bills. The first bill requires that a homeowner pay \(\$ 1800\) plus \(3 \%\) of the assessed home value in taxes. The second bill requires taxes of \(\$ 200\) plus \(8 \%\) of the assessed home value. What price range of home assessment would make the first bill a better deal?

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In solving \(\sqrt{2 x-1}+2=x,\) why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.

This will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$2(x-3)-17=13-3(x+2)$$ is the resulting statement true or false?
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