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

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers.
$-4\sqrt{5}\left(2\sqrt{5}+4\sqrt{12}\right)$
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Brittany Patton
To find:
The product of $-4\sqrt{5}\left(2\sqrt{5}+4\sqrt{12}\right)$ and express answer in simplest radical form:
Concept used:
Distributive property:
$a\left(b+c\right)=ab+ac$
$\sqrt{a×a}=a$
$\sqrt{a}×\sqrt{b}=\sqrt{ab}$
Calculation:
The product of $-4\sqrt{5}\left(2\sqrt{5}+4\sqrt{12}\right)$ can be obtained as,
$-4\sqrt{5}\left(2\sqrt{5}+4\sqrt{12}\right)=-4\sqrt{5}\cdot 2\sqrt{5}-4\sqrt{5}\cdot 4\sqrt{12}$
$=-8\sqrt{5\cdot 5}-16\sqrt{5\cdot 12}$
$=-8\cdot 5-16\sqrt{5\cdot 2\cdot 2\cdot 3}$
$=-40-32\sqrt{15}$
Thus, the product of $-4\sqrt{5}\left(2\sqrt{5}+4\sqrt{12}\right)$ is $-40-32\sqrt{15}$