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

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

Evaluate

$$36$$

Solution Steps

Expand \left(4\sqrt{3}\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{3}\right)^{2}-\left(2\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16\times 3-\left(2\sqrt{3}\right)^{2}$$

Multiply 16 and 3 to get 48.

$$48-\left(2\sqrt{3}\right)^{2}$$

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

$$48-2^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$48-4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$48-4\times 3$$

Multiply 4 and 3 to get 12.

$$48-12$$

Subtract 12 from 48 to get 36.

$$36$$

Factor

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