To simplify the expression \( \sqrt{3}(-9 - \sqrt{2}) \), follow these steps:
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Distribute \( \sqrt{3} \) to both terms inside the parentheses: \[ \sqrt{3} \cdot (-9) + \sqrt{3} \cdot (-\sqrt{2}) \]
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Perform the multiplication:
- For the first term: \[ -9\sqrt{3} \]
- For the second term: \[ -\sqrt{3} \cdot \sqrt{2} = -\sqrt{6} \]
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Combine the terms: \[ -9\sqrt{3} - \sqrt{6} \]
Thus, the simplified expression is: \[ -9\sqrt{3} - \sqrt{6} \]