The expression you've provided is:

$e^{-x} + 2xe^{-x} + x^2 e^{-x}$

This is a combination of exponential and polynomial terms, all of which involve $e^{-x}$.

We can factor out $e^{-x}$ from all the terms:

$e^{-x}(1 + 2x + x^2)$

Now we have the simplified expression:

$e^{-x}(x^2 + 2x + 1)$

Notice that the quadratic $x^2 + 2x + 1$ is a perfect square, so we can rewrite it as:

$e^{-x}(x + 1)^2$

Thus, the simplified form of the expression is:

$e^{-x}(x + 1)^2$

Let me know if you'd like further clarification or if you need help with another problem!

Follow-up questions:

1. How do you differentiate the expression $e^{-x}(x+1)^2$?
2. What are the properties of the function $e^{-x}$?
3. How do you solve for $x$ when $e^{-x}(x+1)^2 = 0$?
4. What is the behavior of $e^{-x}(x+1)^2$ as $x \to \infty$?
5. How do you find the integral of $e^{-x}(x+1)^2$?

Tip: Always try to factor out common terms when simplifying expressions; it often makes it easier to work with!