To simplify the expression $-4x(9x^2 + 3x - 5)$, follow these steps:

1. Distribute $-4x$ to each term inside the parentheses:

$-4x \cdot 9x^2 + -4x \cdot 3x + -4x \cdot (-5)$

2. Multiply each term:

$-4x \cdot 9x^2 = -36x^3$ $-4x \cdot 3x = -12x^2$ $-4x \cdot (-5) = 20x$

3. Combine the results:

$-36x^3 - 12x^2 + 20x$

So, the simplified expression is:

$\boxed{-36x^3 - 12x^2 + 20x}$

Would you like further details or have any questions?

Here are 8 related questions:

1. How would you factor the expression $-36x^3 - 12x^2 + 20x$?
2. What is the derivative of the expression $-36x^3 - 12x^2 + 20x$?
3. What is the integral of the expression $-36x^3 - 12x^2 + 20x$?
4. How would you find the roots of the expression $-36x^3 - 12x^2 + 20x = 0$?
5. How can you factor out the greatest common factor from the expression $-36x^3 - 12x^2 + 20x$?
6. What would happen if you set $x = 1$ in the original expression?
7. How can this expression be used in a real-world application?
8. What is the leading coefficient of the expression $-36x^3 - 12x^2 + 20x$?

Tip: When simplifying expressions, always apply the distributive property carefully to ensure each term is multiplied correctly.