To solve the expression \( 2\sqrt{3} \times (4 - 2\sqrt{2}) \), we can use the distributive property to expand the expression. Let's go through the steps:

1. Distribute \( 2\sqrt{3} \) to each term inside the parentheses:

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

2. Calculate each part of the distribution:

   - First term: \( 2\sqrt{3} \times 4 \)
     
     \[
     2\sqrt{3} \times 4 = 8\sqrt{3}
     \]

   - Second term: \( 2\sqrt{3} \times 2\sqrt{2} \)
     
     \[
     2\sqrt{3} \times 2\sqrt{2} = 4\sqrt{6}
     \]
     
     Here, we use the property of square roots \( \sqrt{a} \times \sqrt{b} = \sqrt{ab} \), so \( \sqrt{3} \times \sqrt{2} = \sqrt{6} \).

3. Substitute these back into the expression:

   \[
   8\sqrt{3} - 4\sqrt{6}
   \]

Therefore, the simplified form of \( 2\sqrt{3} \times (4 - 2\sqrt{2}) \) is:

\[
\boxed{8\sqrt{3} - 4\sqrt{6}}
\]

Would you like further details or have any questions? Here are some related questions to consider:

1. How can we simplify expressions involving other radical terms?
2. What are some examples of using the distributive property with more complex expressions?
3. How do we rationalize the denominator in expressions like \( \frac{1}{\sqrt{2} + \sqrt{3}} \)?
4. What are the properties of square roots that are helpful in simplifying expressions?
5. How can we use these techniques to solve equations involving radicals?

**Tip:** Remember, when multiplying radicals, you can combine them under a single square root sign if the multiplication involves two square roots (e.g., \( \sqrt{a} \times \sqrt{b} = \sqrt{ab} \)).

Discover how to simplify the expression 2√3 × (4 - 2√2) using the distributive property and the multiplication of radicals. This step-by-step solution is ideal for students in Grades 9-10, focusing on key algebraic concepts and properties of square roots.

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