The expression \( x^3 + 27 \) is a sum of cubes, which can be factored using the sum of cubes formula:

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

Here, \( a = x \) and \( b = 3 \) because \( 27 = 3^3 \). So, applying the formula:

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

This is the factorization of the given expression.

Would you like more details or have any questions?

Here are some related questions:
1. How do you factor the difference of cubes?
2. Can the expression \( x^3 + 64 \) be factored similarly?
3. What are the roots of the equation \( x^3 + 27 = 0 \)?
4. How do you expand the product \( (x + 3)(x^2 - 3x + 9) \)?
5. What is the general formula for factoring sums and differences of cubes?
6. How would you factor \( x^3 + 8 \) using the same method?
7. Can the expression \( x^3 + 27 \) be factored further?
8. How is the sum of cubes used in solving polynomial equations?

**Tip:** Recognizing patterns like the sum of cubes can simplify factoring and solving polynomial equations.

Understand how to factorize the expression x^3 + 27 using the sum of cubes formula step-by-step. This problem explores algebraic concepts related to polynomials and factorization, providing a detailed solution and related questions for deeper understanding. Suitable for Grades 9-12 students and anyone interested in algebraic factorization.

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