To simplify the expression \(-4y^2(9y + y^2 - 2)\), follow these steps:

1. Distribute \(-4y^2\) across each term inside the parentheses:
   \[
   -4y^2 \cdot 9y = -36y^3
   \]
   \[
   -4y^2 \cdot y^2 = -4y^4
   \]
   \[
   -4y^2 \cdot (-2) = 8y^2
   \]

2. Combine these results:
   \[
   -4y^2(9y + y^2 - 2) = -4y^4 - 36y^3 + 8y^2
   \]

Thus, the simplified expression is:
\[
-4y^4 - 36y^3 + 8y^2
\]

Would you like more details or have any questions? Here are some related questions to consider:

1. What are the roots of the polynomial \(-4y^4 - 36y^3 + 8y^2\)?
2. How do you factor the expression \(-4y^4 - 36y^3 + 8y^2\)?
3. What is the derivative of the expression?
4. How would you evaluate the expression for a specific value of \(y\)?
5. Can you graph the polynomial, and what would it look like? 

**Tip:** Always check for common factors when simplifying polynomials!

Explore the simplification of the polynomial expression -4y^2(9y + y^2 - 2) step-by-step. This guide covers key algebraic concepts, including distribution and combining like terms. Suitable for students in Grades 7-9.

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