Let's simplify the expression \((4n - 3n^3) - (3n^3 + 4n)\).

### Step-by-step simplification:

1. Distribute the negative sign to each term inside the second parentheses:
   \[
   (4n - 3n^3) - 3n^3 - 4n
   \]
   This becomes:
   \[
   4n - 3n^3 - 3n^3 - 4n
   \]

2. Combine like terms:
   - \(4n - 4n = 0\)
   - \(-3n^3 - 3n^3 = -6n^3\)

3. The simplified expression is:
   \[
   -6n^3
   \]

### Final Answer:
\[
-6n^3
\]

Would you like further explanation on any step?

Here are 5 related questions:
1. How would you simplify \( (5n^2 - 2n^3) - (n^2 + 3n^3) \)?
2. What is the derivative of \( -6n^3 \) with respect to \(n\)?
3. Can you factor \( 6n^3 \)?
4. What happens if \( n = 2 \) in the expression \( -6n^3 \)?
5. How would this problem change if the expression involved \( n^4 \) instead of \( n^3 \)?

**Tip:** Always check for like terms when simplifying expressions!

Learn how to simplify the algebraic expression (4n - 3n^3) - (3n^3 + 4n) with detailed steps. This solution covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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