Answer
$-14+12\sqrt{3w}+6w$.
Work Step by Step
The given expression is
$\Rightarrow (7+\sqrt{3w})(-2+\sqrt{12w})$
Use FOIL method.
$\Rightarrow -14+7\sqrt{12w}-2\sqrt{3w}+\sqrt{36w^2}$
Factor the radicand as perfect square.
$\Rightarrow -14+7\sqrt{4\cdot 3w}-2\sqrt{3w}+\sqrt{36w^2}$
Simplify.
$\Rightarrow -14+7\cdot 2\sqrt{3w}-2\sqrt{3w}+6w$
$\Rightarrow -14+14\sqrt{3w}-2\sqrt{3w}+6w$
Add like terms.
$\Rightarrow -14+12\sqrt{3w}+6w$.
