Let's simplify the given expression:

$-(2x^3 + x^2) + 3(x^3 - 4x^2)$

Step 1: Distribute the negative sign across the first set of parentheses.

$-2x^3 - x^2$

Step 2: Distribute the 3 across the second set of parentheses.

$3x^3 - 12x^2$

Step 3: Combine all the terms from Step 1 and Step 2.

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

Step 4: Combine like terms.

• Combine the $x^3$ terms: $-2x^3 + 3x^3 = x^3$
• Combine the $x^2$ terms: $-x^2 - 12x^2 = -13x^2$

Final Expression:

$x^3 - 13x^2$

So, the simplified form of the expression is $\boxed{x^3 - 13x^2}$.

Would you like more details or have any questions about this solution?

Here are five related questions to expand your understanding:

1. What would the expression look like if $x^3$ had a negative coefficient in both terms?
2. How does the expression change if you factor it?
3. Can you find the roots of the equation $x^3 - 13x^2 = 0$?
4. What happens if you substitute a value for $x$ into the simplified expression?
5. How does the distribution property apply when expanding expressions like this?

Tip: Always remember to distribute negative signs and coefficients carefully when simplifying expressions.