Multiply. $$ 9 \sqrt{5}(\sqrt{15}-\sqrt{6}) $$ Simplify your answer as much as possible.

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UpStudy AI · Accepted Answer

To multiply and simplify the expression $$ 9 \sqrt{5}(\sqrt{15} - \sqrt{6}) $$, follow these steps:

1. **Distribute the Multiplication:**
   $$
   9 \sqrt{5} \cdot \sqrt{15} - 9 \sqrt{5} \cdot \sqrt{6}
   $$

2. **Simplify Each Term Individually:**
   
   - **First Term:**
     $$
     \sqrt{5} \cdot \sqrt{15} = \sqrt{5 \times 15} = \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}
     $$
     So, $$ 9 \sqrt{5} \cdot \sqrt{15} = 9 \times 5\sqrt{3} = 45\sqrt{3} $$.

- **Second Term:**
     $$
     \sqrt{5} \cdot \sqrt{6} = \sqrt{5 \times 6} = \sqrt{30}
     $$
     So, $$ 9 \sqrt{5} \cdot \sqrt{6} = 9\sqrt{30} $$.

3. **Combine the Simplified Terms:**
   $$
   45\sqrt{3} - 9\sqrt{30}
   $$

4. **Factor Out the Common Factor (Optional):**
   $$
   9(5\sqrt{3} - \sqrt{30})
   $$

Both forms are correct, but the fully expanded form is often preferred for clarity.

**Final Answer:**
$$
45\,\sqrt{3}\;-\;9\,\sqrt{30}
$$
The simplified answer is $$ 45\sqrt{3} - 9\sqrt{30} $$.

Multiply. \[ 9 \sqrt{5}(\sqrt{15}-\sqrt{6}) \] Simplify your answer as much as possible.

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