To simplify the expression $x(9x^2 - 3x - 6)$, we distribute $x$ to each term inside the parentheses:

$x(9x^2) - x(3x) - x(6)$

Now, simplify each term:

1. $x \cdot 9x^2 = 9x^3$
2. $x \cdot (-3x) = -3x^2$
3. $x \cdot (-6) = -6x$

Thus, the simplified expression is:

$9x^3 - 3x^2 - 6x$

Would you like any further details or have any questions?

Here are 5 related questions:

1. How would you factor the expression $9x^3 - 3x^2 - 6x$?
2. What happens if you set $9x^3 - 3x^2 - 6x = 0$? How do you solve for $x$?
3. Can you expand $x(9x - 3)(x - 2)$ and compare it to the original expression?
4. How do you find the derivative of $9x^3 - 3x^2 - 6x$?
5. How does the degree of a polynomial affect its graph?

Tip: Always distribute carefully to avoid missing any terms in the process of simplification.