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?

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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!

Discover how to expand the expression (e^x - 1)^2 using binomial expansion. This guide walks through each step, from applying the formula to combining like terms. Learn the key concepts of exponential functions and binomial expansion. Suitable for students in Grades 9-12.

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