To expand $(e^x - 1)^2$, you can apply the binomial expansion formula. Here's the process:

$(e^x - 1)^2 = (e^x - 1)(e^x - 1)$

Now, distribute each term:

$(e^x - 1)(e^x - 1) = e^x \cdot e^x - e^x \cdot 1 - 1 \cdot e^x + 1 \cdot 1$

This simplifies to:

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

Combine like terms:

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

So, the expanded form of $(e^x - 1)^2$ is:

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

Would you like further clarification on any part of this expansion?

---

Here are 5 related questions:

1. How do you expand $(x + y)^2$?
2. What is the derivative of $(e^x - 1)^2$?
3. How do you expand $(e^x + 1)^2$?
4. What is the general binomial expansion formula?
5. How do you simplify expressions involving $e^{x}$?

Tip: When expanding squared binomials, remember to multiply each term in the first binomial by every term in the second binomial!