To simplify the expression [tex]\((6 \sqrt{2})(-3 \sqrt{5})\)[/tex], we will follow a step-by-step approach:
1. Multiply the coefficients:
- Take the constants 6 and -3 and multiply them together:
[tex]\[
6 \times -3 = -18
\][/tex]
2. Multiply the radicals:
- Multiply the square roots under the radical sign:
[tex]\[
\sqrt{2} \times \sqrt{5} = \sqrt{10}
\][/tex]
3. Combine the results:
- Now, putting together the product of the coefficients and the product of the radicals, we get:
[tex]\[
-18 \sqrt{10}
\][/tex]
Thus, the simplified expression is [tex]\(-18\sqrt{10}\)[/tex].
The correct answer is:
B. [tex]\(-18 \sqrt{10}\)[/tex]
