To simplify the expression \(-9a^2(a + 1)\), you need to distribute \(-9a^2\) across each term inside the parentheses.

\[
-9a^2(a + 1) = -9a^2 \cdot a + (-9a^2 \cdot 1)
\]

Now, multiply:

\[
-9a^2 \cdot a = -9a^{3}
\]
\[
-9a^2 \cdot 1 = -9a^2
\]

So, the simplified expression is:

\[
-9a^3 - 9a^2
\]

Would you like more details or have any questions?

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Here are 8 related questions to explore further:

1. How would you factor the expression \(-9a^3 - 9a^2\)?
2. What happens if you substitute \(a = 2\) into the simplified expression?
3. How would you differentiate the expression \(-9a^3 - 9a^2\) with respect to \(a\)?
4. What is the degree of the polynomial \(-9a^3 - 9a^2\)?
5. How would the expression change if the coefficient \(-9\) were replaced with a positive value?
6. Can you factor out \(-9a^2\) from the original expression in a different way?
7. What is the sum of the coefficients in the simplified expression?
8. How does the expression \(-9a^2(a + 1)\) relate to the distributive property?

**Tip:** Always distribute the sign (positive or negative) when expanding expressions inside parentheses.

Learn how to simplify the expression -9a^2(a + 1) step-by-step with detailed explanations and examples. This problem covers algebraic concepts such as the distributive property and polynomial simplification. Suitable for students in Grades 7-9.

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