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

Learn how to simplify the expression (√3 - 1)^2 step by step using the binomial expansion formula. This tutorial walks through algebraic concepts, radicals, and the binomial theorem. Perfect for students in Grades 8-10.

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