Question

Multiply
V6(v2-2v7)
Simplify as much as possible

Answer 1

To multiply \( \sqrt{6}(\sqrt{2} - 2\sqrt{7}) \), we'll distribute \( \sqrt{6} \) to each term inside the parentheses:

\[
\sqrt{6} \cdot \sqrt{2} - \sqrt{6} \cdot 2\sqrt{7}
\]

Now, we can simplify each term:

1. For the first term:
\[
\sqrt{6} \cdot \sqrt{2} = \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}
\]

2. For the second term:
\[
\sqrt{6} \cdot 2\sqrt{7} = 2\sqrt{42}
\]

Putting it all together, we have:

\[
2\sqrt{3} - 2\sqrt{42}
\]

We can factor out the common factor of 2:

\[
2(\sqrt{3} - \sqrt{42})
\]

Therefore, the simplified expression is:

\[
\boxed{2(\sqrt{3} - \sqrt{42})}
\]