The expression provided is \( \boxed{x^3 - 27} \). This can be factored as a difference of cubes. The formula for factoring the difference of cubes is:

\[
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
\]

In this case:
- \( a = x \)
- \( b = 3 \) (since \( 3^3 = 27 \))

Using the formula:

\[
x^3 - 27 = (x - 3)(x^2 + 3x + 9)
\]

So, the factored form of \( x^3 - 27 \) is \( \boxed{(x - 3)(x^2 + 3x + 9)} \).

Would you like to explore this factorization in more detail, or do you have any other questions?

Here are some related questions you might find interesting:
1. How do you factor a sum of cubes?
2. What are the roots of the equation \( x^3 - 27 = 0 \)?
3. How can you use the quadratic formula to solve \( x^2 + 3x + 9 = 0 \)?
4. What is the geometric interpretation of the difference of cubes?
5. How does the difference of cubes formula relate to polynomial division?

**Tip:** When factoring, always check if the expression is a difference or sum of cubes; they have specific formulas that simplify the process.

Understand how to factor the expression x^3 - 27 using the difference of cubes formula. This problem involves algebraic concepts such as factoring polynomials and specific formulas for cubes. Suitable for advanced high school students.

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