Question

Let's review each step of Sara's work to check for errors.

### Given Expression:
(2x³ - 7x² + 4x) - (9x - 5x³ + 9x²)

### Step 1:
Sara rewrote the expression as:
2x³ - 7x² + 4x - 9x - 5x³ + 9x²

**Correction:** This step is correct. She has properly distributed the negative sign across the second polynomial.

### Step 2:
Sara then combined like terms:
2x³ - 5x³ - 7x² + 9x² + 4x - 9x

Let's combine the like terms:
- For \(x³\):
\(2x³ - 5x³ = -3x³\)
- For \(x²\):
\(-7x² + 9x² = 2x²\)
- For \(x\):
\(4x - 9x = -5x\)

So the correct combination of like terms should yield:
-3x³ + 2x² - 5x.

**Correction:** This step is also correct.

### Step 3:
Sara concluded with:
−3x³ + 2x² − 5x

**Final Check:** She accurately combined the like terms in the previous step, which means her final answer is indeed correct.

### Conclusion:
Sara's work is correct:
- **Final Answer:** \(−3x³ + 2x² − 5x\)

Her friend should tell her that she made no errors in her work; the solution is correct.