Let's simplify the expression:
[tex]\[
(2 - 5 \sqrt{6}) \cdot 3 \sqrt{2}
\][/tex]
First, distribute [tex]\(3 \sqrt{2}\)[/tex] to both terms inside the parentheses:
1. First Term:
[tex]\[
2 \cdot 3 \sqrt{2} = 6 \sqrt{2}
\][/tex]
2. Second Term:
[tex]\[
- 5 \sqrt{6} \cdot 3 \sqrt{2}
\][/tex]
[tex]\[
- 5 \cdot 3 \sqrt{6 \cdot 2} = - 15 \sqrt{12}
\][/tex]
Now, combine the two terms:
[tex]\[
6 \sqrt{2} - 15 \sqrt{12}
\][/tex]
For further simplification, we can simplify [tex]\(\sqrt{12}\)[/tex]:
[tex]\[
\sqrt{12} = \sqrt{4 \cdot 3} = 2 \sqrt{3}
\][/tex]
Thus, substituting back:
[tex]\[
- 15 \sqrt{12} = - 15 \cdot 2 \sqrt{3} = - 30 \sqrt{3}
\][/tex]
Finally, the expression simplifies to:
[tex]\[
6 \sqrt{2} - 30 \sqrt{3}
\][/tex]
So, the final simplified form of the given expression is:
\[
6 \sqrt{2} - 30 \sqrt{3}
\}
