To determine whether the student is correct, let's look at their work step by step.
1. **Original expression**:
\((2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)\)
2. **Step 1**:
Distribute the negative sign correctly:
\[
2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2
\]
This is the correct rearrangement.
3. **Step 2**:
Combine like terms:
- For \(x^3\): \(2x^3 + 5x^3 = 7x^3\)
- For \(x^2\): \(-7x^2 - 9x^2 = -16x^2\)
- For \(x\): \(4x - 9x = -5x\)
Correctly combining them, we should have:
\[
(2x^3 + 5x^3) + (-7x^2 - 9x^2) + (4x - 9x) = 7x^3 - 16x^2 - 5x
\]
4. **Step 3**:
The final answer should be:
\[
7x^3 - 16x^2 - 5x
\]
The student's final answer was \(-3x^3 + 2x^2 - 5x\). Clearly, there is a discrepancy.
**Conclusion**:
The student is **incorrect**. They made the error in **Step 2** when combining like terms. The correct coefficients, after correctly arranging the terms, should yield \(7x^3 - 16x^2 - 5x\) instead of \(-3x^3 + 2x^2 - 5x\).