Solve (-2sqrt{3})^2*(2sqrt{x})^2+1/4sqrt{4}(-sqrt{3})

$$( - 2 \sqrt { 3 } ) ^ { 2 } \cdot ( 2 \sqrt { x } ) ^ { 2 } + \frac { 1 } { 4 } \sqrt { 4 } ( - \sqrt { 3 } )$$

Evaluate

$$48x-\frac{\sqrt{3}}{2}$$

Solution Steps

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

$$\left(-2\right)^{2}\left(\sqrt{3}\right)^{2}\times \left(2\sqrt{x}\right)^{2}+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

Calculate -2 to the power of 2 and get 4.

$$4\left(\sqrt{3}\right)^{2}\times \left(2\sqrt{x}\right)^{2}+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

The square of \sqrt{3} is 3.

$$4\times 3\times \left(2\sqrt{x}\right)^{2}+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

Multiply 4 and 3 to get 12.

$$12\times \left(2\sqrt{x}\right)^{2}+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

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

$$12\times 2^{2}\left(\sqrt{x}\right)^{2}+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

Calculate 2 to the power of 2 and get 4.

$$12\times 4\left(\sqrt{x}\right)^{2}+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

Calculate \sqrt{x} to the power of 2 and get x.

$$12\times 4x+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

Multiply 12 and 4 to get 48.

$$48x+\frac{1}{4}\sqrt{4}\left(-\sqrt{3}\right)$$

Calculate the square root of 4 and get 2.

$$48x+\frac{1}{4}\times 2\left(-\sqrt{3}\right)$$

Multiply \frac{1}{4} and 2 to get \frac{1}{2}.

$$48x+\frac{1}{2}\left(-\sqrt{3}\right)$$

Factor

$$\frac{96x-\sqrt{3}}{2}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{64\left(\sqrt{3}\right)^{2}\left(\sqrt{x}\right)^{2}-2\sqrt{3}}{4}$$