Solve {l}{(5+sqrt{3})4sqrt{3}}{-(5-sqrt{3})4sqrt{3}}

$$\left. \begin{array} { l } { ( 5 + \sqrt { 3 } ) 4 \sqrt { 3 } } \\ { - ( 5 - \sqrt { 3 } ) 4 \sqrt { 3 } } \end{array} \right.$$

Evaluate

$$24$$

Solution Steps

Use the distributive property to multiply 4 by 5+\sqrt{3}.

$$\left(20+4\sqrt{3}\right)\sqrt{3}-4\left(5-\sqrt{3}\right)\sqrt{3}$$

Use the distributive property to multiply 20+4\sqrt{3} by \sqrt{3}.

$$20\sqrt{3}+4\left(\sqrt{3}\right)^{2}-4\left(5-\sqrt{3}\right)\sqrt{3}$$

The square of \sqrt{3} is 3.

$$20\sqrt{3}+4\times 3-4\left(5-\sqrt{3}\right)\sqrt{3}$$

Multiply 4 and 3 to get 12.

$$20\sqrt{3}+12-4\left(5-\sqrt{3}\right)\sqrt{3}$$

Use the distributive property to multiply -4 by 5-\sqrt{3}.

$$20\sqrt{3}+12+\left(-20+4\sqrt{3}\right)\sqrt{3}$$

Use the distributive property to multiply -20+4\sqrt{3} by \sqrt{3}.

$$20\sqrt{3}+12-20\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$20\sqrt{3}+12-20\sqrt{3}+4\times 3$$

Multiply 4 and 3 to get 12.

$$20\sqrt{3}+12-20\sqrt{3}+12$$

Combine 20\sqrt{3} and -20\sqrt{3} to get 0.

$$12+12$$

Add 12 and 12 to get 24.

$$24$$

Factor

$$2^{3}\times 3$$