Answer
$34 - 15\sqrt{5}$
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,
$\sqrt{a} \cdot \sqrt{b}=\sqrt{ab}$
(3) $(a+b)(c-d) = a(c-d) + b(c-d)$
Use rule (3) above to obtain:
$=6(9 - 4\sqrt{5})+ \sqrt{5}(9 - 4\sqrt{5})$
Use rules (1) and (2) above then simplify to obtain:
$=6(9) - 6(4\sqrt{5}) + \sqrt{5}(9) - \sqrt{5}(4\sqrt{5})
\\=54 - 24\sqrt{5} + 9\sqrt{5}-4\sqrt{5(5)}
\\=54 + (-24+9)\sqrt{5} - 4\sqrt{25}
\\=54 + (-15\sqrt{5}) - 4(5)
\\=54 - 15\sqrt{5}-20
\\=34 - 15\sqrt{5}$
