To factor the expression \(x^3 - y^3\), we use the difference of cubes formula:

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

Here, \(a = x\) and \(b = y\). Applying the formula, we get:

\[
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
\]

So, the factored form of \(x^3 - y^3\) is:

\[
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
\]

Would you like further details or have any questions about this factorization?

Here are some related questions to explore this topic further:

1. How would you factor \(x^3 + y^3\)?
2. What is the factored form of \(a^3 - b^3\) if \(a = 2\) and \(b = 3\)?
3. How can you apply the difference of cubes formula to solve \(27x^3 - 8y^3\)?
4. What is the expanded form of \((x - y)(x^2 + xy + y^2)\)?
5. Can you factor \(x^3 - 1\) using the difference of cubes formula?

**Tip:** Remember that the difference of cubes formula can be very useful in simplifying expressions and solving equations that involve cubic terms.

Understand how to factorize the expression x^3 - y^3 using the difference of cubes formula. This problem involves key algebraic concepts and techniques for solving cubic equations. Suitable for advanced high school students and college-level algebra courses.

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