Let's expand and simplify the expression -\sqrt{2}(3-\sqrt{2}) step by step.
Step 1: Understand the expression
The expression means multiplying -\sqrt{2} with each term inside the bracket (3 and -\sqrt{2}).
Step 2: Distribute -√2 to each term in the bracket
-\sqrt{2} × 3 = -3\sqrt{2}
-\sqrt{2} × (-\sqrt{2}) = + (\sqrt{2} × \sqrt{2}) = +2
Note: When multiplying two surds with the same number under the root, \(\sqrt{a} \times \sqrt{a} = a\)
Step 3: Write the expression with the multiplied terms
-3\sqrt{2} + 2
Step 4: Final simplified expression
So, the simplified form of -\sqrt{2}(3-\sqrt{2}) is:
2 - 3\sqrt{2}
This is the final answer!