To solve the expression \((1 - \sqrt{3})^2\), we can expand it using the formula for the square of a binomial:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

Here, \(a = 1\) and \(b = \sqrt{3}\). Let's apply the formula:

\[
(1 - \sqrt{3})^2 = 1^2 - 2(1)(\sqrt{3}) + (\sqrt{3})^2
\]

Now, calculate each term:

- \(1^2 = 1\)
- \(2(1)(\sqrt{3}) = 2\sqrt{3}\)
- \((\sqrt{3})^2 = 3\)

Putting it all together:

\[
(1 - \sqrt{3})^2 = 1 - 2\sqrt{3} + 3
\]

Simplify further:

\[
1 - 2\sqrt{3} + 3 = 4 - 2\sqrt{3}
\]

So, the simplified result is:

\[
\boxed{4 - 2\sqrt{3}}
\]

Would you like a detailed explanation on any part of this solution? Here are five related questions to consider:

1. How would you expand \((2 + \sqrt{5})^2\)?
2. What is the value of \((\sqrt{2} - \sqrt{3})^2\)?
3. Can you solve \((1 + \sqrt{2})(1 - \sqrt{2})\) using the difference of squares?
4. How does the formula \((a - b)^2\) apply to complex numbers?
5. How do you simplify the expression \(\sqrt{a^2 + b^2}\) where \(a\) and \(b\) are real numbers?

**Tip:** When squaring a binomial, always remember to use the formula \((a \pm b)^2 = a^2 \pm 2ab + b^2\) to ensure accuracy.

Explore the step-by-step solution to (1 - √3)^2 using the binomial theorem. Understand how to expand and simplify binomial squares, essential for advanced high school mathematics. Detailed explanations and practice questions included.

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