The theorem that relates to the factorization of expressions like the one you provided, particularly involving cubes, is known as the **Sum and Difference of Cubes Theorem**.

### Sum and Difference of Cubes Theorem:
- **Sum of Cubes**: 
  \[
  a^3 + b^3 = (a + b)(a^2 - ab + b^2)
  \]
- **Difference of Cubes**: 
  \[
  a^3 - b^3 = (a - b)(a^2 + ab + b^2)
  \]

This theorem was applied in the factorization of \( x^3 + 27 \) (where \( x^3 + 3^3 \) is a sum of cubes) into \( (x + 3)(x^2 - 3x + 9) \).

Would you like more details or have any other questions?

Here are 5 related questions that could expand your understanding:
1. How can you use the Sum of Cubes Theorem to factor \( x^3 + 64 \)?
2. What is the Difference of Cubes Theorem, and how does it apply to \( x^3 - 27 \)?
3. Can the Sum and Difference of Cubes be used in higher dimensions or different algebraic structures?
4. How can the Sum of Cubes formula be derived?
5. What are some real-world applications of the Sum and Difference of Cubes Theorem?

**Tip**: When learning factorization theorems like Sum and Difference of Cubes, practice by identifying the cube terms in various polynomials and applying the theorem directly to reinforce the concept.

Explore the Sum and Difference of Cubes Theorem, including its application in algebraic factorization. Learn how to apply the theorem to problems like factoring x^3 + 27 and x^3 - 8. Suitable for advanced high school students and anyone interested in algebraic factorization theorems.

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