Question

simplify.
$5\sqrt{3}\left(6\sqrt{10} - 6\sqrt{3}\
ight)$

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b - c)=ab - ac\), where \(a = 5\sqrt{3}\), \(b=6\sqrt{10}\) and \(c = 6\sqrt{3}\). So we get \(5\sqrt{3}\times6\sqrt{10}-5\sqrt{3}\times6\sqrt{3}\).

Step2: Multiply the coefficients and the radicals

For the first term \(5\sqrt{3}\times6\sqrt{10}\), we multiply the coefficients \(5\times6 = 30\) and the radicals \(\sqrt{3}\times\sqrt{10}=\sqrt{3\times10}=\sqrt{30}\), so the first term is \(30\sqrt{30}\).

For the second term \(5\sqrt{3}\times6\sqrt{3}\), we multiply the coefficients \(5\times6=30\) and the radicals \(\sqrt{3}\times\sqrt{3}=\sqrt{3\times3} = 3\), so the second term is \(30\times3=90\).

Step3: Combine the terms

Putting it together, we have \(30\sqrt{30}-90\).

Answer:

\(30\sqrt{30}-90\)