Find the following products and express answers in simplest radical form. All va

To find:
The product of ${\displaystyle -4\sqrt{5}(2\sqrt{5}+4\sqrt{12})}$ and express answer in simplest radical form:
Concept used:
Distributive property:
${\displaystyle a(b+c)=ab+ac}$
Radical property:
${\displaystyle \sqrt{a\times a}=a}$
${\displaystyle \sqrt{a}\times \sqrt{b}=\sqrt{ab}}$
Calculation:
The product of ${\displaystyle -4\sqrt{5}(2\sqrt{5}+4\sqrt{12})}$ can be obtained as,
${\displaystyle -4\sqrt{5}(2\sqrt{5}+4\sqrt{12})=-4\sqrt{5}\cdot 2\sqrt{5}-4\sqrt{5}\cdot 4\sqrt{12}}$
${\displaystyle =-8\sqrt{5\cdot 5}-16\sqrt{5\cdot 12}}$
${\displaystyle =-8\cdot 5-16\sqrt{5\cdot 2\cdot 2\cdot 3}}$
${\displaystyle =-40-32\sqrt{15}}$
Thus, the product of ${\displaystyle -4\sqrt{5}(2\sqrt{5}+4\sqrt{12})}$ is ${\displaystyle -40-32\sqrt{15}}$