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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.

Learn how to simplify the polynomial expression -2x^3 + x^2 + 3(x^3 - 4x^2) step-by-step. This problem involves polynomial simplification and the distribution property in algebra. Suitable for high school students.

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