Let's simplify the given expression:

$y = (-1)e^{-x} + (-2)e^{-2x} - e^{-2x} \sin(x)$

Step-by-step simplification:

1. Distribute the negative signs: $y = -e^{-x} - 2e^{-2x} - e^{-2x} \sin(x)$

2. Group terms with common factors if possible:

   The terms involving $e^{-2x}$ can be grouped: $y = -e^{-x} - e^{-2x} (2 + \sin(x))$

Final simplified form:

$y = -e^{-x} - e^{-2x} (2 + \sin(x))$

This is the simplified expression.

Would you like further clarification or have any questions?

Here are 5 related questions:

1. How can I expand the expression involving $e^{-2x}$ and $\sin(x)$?
2. What is the behavior of the function as $x \to \infty$?
3. How would the function change if we added a constant to the expression?
4. Can you solve for $x$ when $y = 0$?
5. How do you handle other exponential functions in such expressions?

Tip: When simplifying exponential expressions, look for common factors (like $e^{-2x}$) to group terms and make the expression more compact.