Sara's friend should check her solution step by step to ensure that each operation is performed correctly. Let's analyze the steps provided.
### Given expression:
\((2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)\)
### Step 1:
Sara rewrote the expression as:
\[ 2x^3 - 7x^2 + 4x - 9x - 5x^3 + 9x^2 \]
**This step is correct.** She appropriately distributed the negative sign.
### Step 2:
Sara rearranged the terms to combine them:
\[ 2x^3 - 5x^3 - 7x^2 + 9x^2 + 4x - 9x \]
**This step is also correct.** She properly grouped the like terms (although the order doesn't affect the result).
### Step 3:
Sara simplified the expression to:
\[ -3x^3 + 2x^2 - 5x \]
**This step contains an error.**
### Error:
- In combining the \(x^2\) terms, she computed \( -7x^2 + 9x^2 \) incorrectly. The correct calculation should be:
\[
-7x^2 + 9x^2 = 2x^2
\]
- However, the subtraction of the \(x\) terms \(4x - 9x\) is correctly calculated as \(-5x\).
So, the total from Step 3 should be:
\[
-3x^3 + 2x^2 - 5x
\]
**Final Conclusion:**
Sara's friend should tell her that the steps were mostly correct, but she should double-check her calculations. If we specifically focus on the polynomials, she needs to ensure she correctly combines like terms. In this case, **there was no error** in Step 3, as her final answer of \(-3x^3 + 2x^2 - 5x\) is indeed correct.
**Final Answer to Friend's Response:**
"Sara, your solution is correct. The way you subtracted and combined the terms is accurate. There was no error in your steps. You have calculated the final expression correctly as \(-3x^3 + 2x^2 - 5x\)."