The expression given is:

$\sin^3(x) - \cos^3(x)$

This is a difference of cubes, which can be factored using the identity:

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

Here, $a = \sin(x)$ and $b = \cos(x)$, so applying the identity, we get:

$\sin^3(x) - \cos^3(x) = (\sin(x) - \cos(x))(\sin^2(x) + \sin(x)\cos(x) + \cos^2(x))$

We know that $\sin^2(x) + \cos^2(x) = 1$, so the expression simplifies further:

$\sin^3(x) - \cos^3(x) = (\sin(x) - \cos(x))(1 + \sin(x)\cos(x))$

Thus, the factored and simplified form of the expression is:

$(\sin(x) - \cos(x))(1 + \sin(x)\cos(x))$

Would you like more details or have any further questions?

Here are 5 related questions to explore:

1. How do you factor the sum of cubes, $a^3 + b^3$?
2. What is the geometric interpretation of the sine and cosine functions?
3. How can you use trigonometric identities to simplify other expressions?
4. What are some real-world applications of the sine and cosine functions?
5. How does the Pythagorean identity $\sin^2(x) + \cos^2(x) = 1$ apply in other trigonometric problems?

Tip: Always look for identities, such as the Pythagorean identity, when simplifying trigonometric expressions!