Simplify the following expression:
\$(2\sqrt(3) + \sqrt(12)) \times (\sqrt(3) - \sqrt(6))\$

Identify the Expression:

\$(2\sqrt(3) + \sqrt(12)) \times (\sqrt(3) - \sqrt(6))\$

Simplify \$\sqrt(12)\$

\$\sqrt(12) = \sqrt(4 \times 3) = 2\sqrt(3)\$

\$ (2\sqrt(3) + 2\sqrt(3)) \times (\sqrt(3) - \sqrt(6))\$

Combine Like Terms:

\$(2\sqrt(3)) + (2\sqrt(3)) = 4\sqrt(3)\$

\$4\sqrt(3) \times (\sqrt(3) - \sqrt(6))\$

Distribute \$4\sqrt(3)\$

\$4\sqrt(3) \times \sqrt(3) - 4\sqrt(3) \times \sqrt(6)\$

Simplify Each Term:

\$4\sqrt(3) \times \sqrt(3) = 4 \times 3 = 12\$

\$4\sqrt(3) \times \sqrt(6) = 4 \times \sqrt(18) = 4 \times 3\sqrt(2) = 12\sqrt(2)\$

Combine the Simplified Terms:

\$12 - 12\sqrt(2)\$

Therefore, the simplified expression is \$12 - 12\sqrt(2)\$.

This option is Incorrect, as it doesn’t match our result, which includes a subtraction term

\$12\sqrt(2)\$

This option is Incorrect, as it only represents part of the final result and misses the constant termt

\$- 12\sqrt(2)\$

This option is Correct, as it exactly matches the simplified expression

\$12 - 12\sqrt(2)\$

This option is Incorrect, as our simplification does not yield any term with \$12\sqrt(3)\$

\$12\sqrt(3)\$

Option

C

Can you summarize what you’ve understood in the above steps?