To simplify $(\sqrt{3} - 1)^2$, follow these steps:

Step 1: Use the binomial expansion formula:

$(a - b)^2 = a^2 - 2ab + b^2$ Here, $a = \sqrt{3}$ and $b = 1$.

Step 2: Apply the formula:

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

Step 3: Simplify each term:

$(\sqrt{3})^2 = 3,\quad 2(\sqrt{3})(1) = 2\sqrt{3},\quad (1)^2 = 1$

Step 4: Combine the results:

$(\sqrt{3} - 1)^2 = 3 - 2\sqrt{3} + 1 = 4 - 2\sqrt{3}$

So, $(\sqrt{3} - 1)^2 = 4 - 2\sqrt{3}$.

Would you like further details or have any questions?

Here are five related questions:

1. What is the value of $(\sqrt{2} + 1)^2$?
2. How do you expand $(a + b)^2$?
3. Can you simplify $(\sqrt{5} - 2)^2$?
4. What is the general formula for $(a - b)^3$?
5. What happens when you square a complex number?

Tip: The difference of squares and binomial expansion are very useful for simplifying expressions like $(\sqrt{3} - 1)^2$.