Let's simplify the given polynomial expression:

$(-4x^3 + 9x^2 + 2x) + (-6x^3 + 7x - 2)$

Step 1: Distribute and Combine Like Terms

Group terms based on their powers of $x$:

• $x^3$ terms: $-4x^3 - 6x^3 = -10x^3$
• $x^2$ terms: $9x^2$ (there's no other $x^2$ term, so it remains $+9x^2$)
• $x$ terms: $2x + 7x = 9x$
• Constant terms: $-2$

Step 2: Write the Simplified Expression

After combining like terms, we have: $-10x^3 + 9x^2 + 9x - 2$

Step 3: Match with the Options

The correct answer is: $\text{Option A: } -10x^3 + 9x^2 + 9x - 2$

Would you like more details on this solution or have any questions?

Here are five additional questions to deepen your understanding:

1. How do you add or subtract polynomials with multiple variables?
2. What steps would you take if the terms were presented in a different order?
3. How do you identify like terms in polynomial expressions?
4. Can you explain why combining like terms is essential in polynomial simplification?
5. What happens if you incorrectly combine terms with different powers?

Tip: Always double-check each term’s sign when combining like terms; it's easy to make mistakes with negative signs.