Answer
$12\sqrt{2} - 6$
Work Step by Step
RECALL:
(1) Distributive Property:
For any real numbers a, b, and c,
$a(b−c)=ab−ac$
(2) For any real numbers real numbers a and b within the domain,
$\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{ab}$
(3) $\sqrt{a} \cdot \sqrt{a} = a, a\ge 0$
Use rule (1) above to obtain:
$=\sqrt{3}(4\sqrt{6}) -\sqrt{3} \cdot 2\sqrt{3}$
Use rule (2) above to obtain:
$=4\sqrt{18} - 2\sqrt{9}
\\=4\sqrt{9\cdot2} - 2\sqrt{3^2}
\\=4\sqrt{3^2 \cdot 2} - 2\sqrt{3^2}$
Simplify each radical to obtain:
$=4(3)\sqrt{2} - 2(3)
\\=12\sqrt{2} - 6$
