Solve left(2xright)^2-{left(x/2*sqrt{3}right)}^2

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

Evaluate

$$\frac{47x^{2}}{12}$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

Rationalize the denominator of \frac{x}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

$$4x^{2}-\left(\frac{x\sqrt{3}}{6}\right)^{2}$$

To raise \frac{x\sqrt{3}}{6} to a power, raise both numerator and denominator to the power and then divide.

$$4x^{2}-\frac{\left(x\sqrt{3}\right)^{2}}{6^{2}}$$

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

$$4x^{2}-\frac{x^{2}\left(\sqrt{3}\right)^{2}}{6^{2}}$$

The square of \sqrt{3} is 3.

$$4x^{2}-\frac{x^{2}\times 3}{6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$4x^{2}-\frac{x^{2}\times 3}{36}$$

Divide x^{2}\times 3 by 36 to get x^{2}\times \frac{1}{12}.

$$4x^{2}-x^{2}\times \frac{1}{12}$$

Multiply -1 and \frac{1}{12} to get -\frac{1}{12}.

$$4x^{2}-\frac{1}{12}x^{2}$$

Combine 4x^{2} and -\frac{1}{12}x^{2} to get \frac{47}{12}x^{2}.

$$\frac{47}{12}x^{2}$$

Expand

$$\frac{47x^{2}}{12}$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

Rationalize the denominator of \frac{x}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

$$4x^{2}-\left(\frac{x\sqrt{3}}{6}\right)^{2}$$

To raise \frac{x\sqrt{3}}{6} to a power, raise both numerator and denominator to the power and then divide.

$$4x^{2}-\frac{\left(x\sqrt{3}\right)^{2}}{6^{2}}$$

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

$$4x^{2}-\frac{x^{2}\left(\sqrt{3}\right)^{2}}{6^{2}}$$

The square of \sqrt{3} is 3.

$$4x^{2}-\frac{x^{2}\times 3}{6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$4x^{2}-\frac{x^{2}\times 3}{36}$$

Divide x^{2}\times 3 by 36 to get x^{2}\times \frac{1}{12}.

$$4x^{2}-x^{2}\times \frac{1}{12}$$

Multiply -1 and \frac{1}{12} to get -\frac{1}{12}.

$$4x^{2}-\frac{1}{12}x^{2}$$

Combine 4x^{2} and -\frac{1}{12}x^{2} to get \frac{47}{12}x^{2}.

$$\frac{47}{12}x^{2}$$