The given expression is:

$\frac{8x^3}{x^2 - 4}$

This can be simplified by factoring the denominator. Notice that the denominator is a difference of squares:

$x^2 - 4 = (x - 2)(x + 2)$

So the expression becomes:

$\frac{8x^3}{(x - 2)(x + 2)}$

There are no common factors between the numerator and denominator that can be cancelled out. Therefore, the simplified form is:

$\frac{8x^3}{(x - 2)(x + 2)}$

If you need further details or a specific type of transformation (e.g., partial fraction decomposition or domain analysis), let me know!

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Here are 5 related questions to expand your understanding:

1. How do you factor the difference of squares?
2. What is the domain of the function $\frac{8x^3}{x^2 - 4}$?
3. How do you perform polynomial long division when the degree of the numerator is greater than the denominator?
4. What happens to the function as $x$ approaches 2 or -2?
5. How would you simplify rational expressions with higher degrees?

Tip: Always look for common factoring patterns (like the difference of squares or perfect square trinomials) to simplify rational expressions.