Solve (2sqrt{3})^2-(4sqrt{2})^2

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

Evaluate

$$-20$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

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

Expand \left(4\sqrt{2}\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$12-16\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$12-16\times 2$$

Multiply 16 and 2 to get 32.

$$12-32$$

Subtract 32 from 12 to get -20.

$$-20$$

Factor

$$-20$$