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!