To simplify the expression [tex]\((6 \sqrt{2})(-3 \sqrt{5})\)[/tex], follow these steps:
1. Multiply the coefficients: The coefficients here are 6 and -3. When you multiply these together:
[tex]\[
6 \times -3 = -18
\][/tex]
2. Multiply the square roots: The square roots here are [tex]\(\sqrt{2}\)[/tex] and [tex]\(\sqrt{5}\)[/tex]. When multiplying square roots, you can multiply the numbers inside the square roots together:
[tex]\[
\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} = \sqrt{10}
\][/tex]
3. Combine the results: Now, combine the result of the coefficients and the result of the square roots:
[tex]\[
(6 \sqrt{2})(-3 \sqrt{5}) = -18 \sqrt{10}
\][/tex]
Hence, the simplified form of the expression [tex]\((6 \sqrt{2})(-3 \sqrt{5})\)[/tex] is:
[tex]\[
\boxed{-18 \sqrt{10}}
\][/tex]
So, the correct answer is:
B. [tex]\(-18 \sqrt{10}\)[/tex]
