Answer
$25 - 2\sqrt{5}$
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:
$=4(10 - 3\sqrt{5})+ \sqrt{5}(10 - 3\sqrt{5})$
Use rules (1) and (2) above then simplify to obtain:
$=4(10) - 4(3\sqrt{5}) + \sqrt{5}(10) - \sqrt{5}(3\sqrt{5})
\\=40 - 12\sqrt{5} + 10\sqrt{5}-3\sqrt{5(5)}
\\=40 + (-12+10)\sqrt{5} - 3\sqrt{25}
\\=40 + (-2\sqrt{5}) - 3(5)
\\=40 - 2\sqrt{5}-15
\\=25 - 2\sqrt{5}$
