Solve (3)(-sqrt{5})^2-(2sqrt{3})^2

$$( 3 ) ( - \sqrt { 5 } ) ^ { 2 } - ( 2 \sqrt { 3 } ) ^ { 2 }$$

Evaluate

$$3$$

Solution Steps

Calculate -\sqrt{5} to the power of 2 and get \left(\sqrt{5}\right)^{2}.

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

Expand \left(2\sqrt{3}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$3\left(\sqrt{5}\right)^{2}-12$$

The square of \sqrt{5} is 5.

$$3\times 5-12$$

Multiply 3 and 5 to get 15.

$$15-12$$

Subtract 12 from 15 to get 3.

$$3$$

Factor

$$3$$