https://file.aiquickdraw.com/mathbot/file/1729447608197iebu3z1o.jpg

Let's solve the expression:

You are asked to **expand and simplify** \((\sqrt{12} - \sqrt{3})^2\).

1. **Step 1: Simplify the square roots.**

   \[
   \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
   \]
   \[
   \sqrt{3} = \sqrt{3}
   \]

   So the expression becomes:
   \[
   (2\sqrt{3} - \sqrt{3})^2
   \]

2. **Step 2: Factor the terms.**

   Now, let's factor out \(\sqrt{3}\) from the terms inside the bracket:
   \[
   \sqrt{3}(2 - 1) = \sqrt{3}(1) = \sqrt{3}
   \]

   So the expression becomes:
   \[
   (\sqrt{3})^2
   \]

3. **Step 3: Simplify the square.**

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

Thus, the simplified result of \((\sqrt{12} - \sqrt{3})^2\) is **3**.

Would you like more details or do you have any questions? 

Here are 5 related questions for further practice:
1. Expand and simplify \((\sqrt{8} + \sqrt{2})^2\).
2. Simplify \((\sqrt{18} - \sqrt{2})^2\).
3. What is \(\sqrt{50} + \sqrt{2}\)?
4. Expand \((3 + \sqrt{5})^2\).
5. What is the simplified form of \(\sqrt{20} - \sqrt{5}\)?

**Tip:** Always simplify square roots as much as possible before expanding!

Expand and simplify the expression (√12 − √3)². This solution involves simplifying square roots and using the expansion formula (a - b)² = a² - 2ab + b². Suitable for students in Grades 9-10.

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