Thank you for the clarification. Let's go through the problem again with the corrected term \(7m^3n\).

### Given expression:
\[
m^3 + 7m^3n - 6mn + n^2 + 2m^3 + 8m^3n - mn + 2n^3
\]

### Step 1: Identify and combine like terms

- **\(m^3\)** terms: \(m^3\) and \(2m^3\)
- **\(m^3n\)** terms: \(7m^3n\) and \(8m^3n\)
- **\(mn\)** terms: \(-6mn\) and \(-mn\)
- **\(n^2\)** term: \(n^2\)
- **\(n^3\)** term: \(2n^3\)

### Step 2: Combine the like terms

\[
(m^3 + 2m^3) + (7m^3n + 8m^3n) + (-6mn - mn) + n^2 + 2n^3
\]

Simplifying each group:

\[
3m^3 + 15m^3n - 7mn + n^2 + 2n^3
\]

### Final Simplified Expression:
\[
3m^3 + 15m^3n - 7mn + n^2 + 2n^3
\]

This is the correct simplified form of the expression with the corrected terms.

Do you have any further questions or need more details? Here are five related questions:

1. How can you check if your polynomial has been simplified correctly?
2. What strategies can help identify like terms more efficiently?
3. How do you expand and simplify polynomials involving multiple variables?
4. What is the difference between monomials, binomials, and trinomials?
5. How can you apply polynomial expressions to real-world problems?

**Tip:** When dealing with multiple variables and terms, it's helpful to rewrite the expression with like terms grouped together before simplifying.

Learn how to simplify the polynomial expression 7m^3n with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomials and simplification of expressions involving multiple variables. Suitable for high school students and those preparing for advanced algebra exams.

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