Solve x^2+(frac{4sqrt{6}}{3}x)^2

$$x ^ { 2 } + ( \frac { 4 \sqrt { 6 } } { 3 } x ) ^ { 2 }$$

Evaluate

$$\frac{35x^{2}}{3}$$

Solution Steps

Express \frac{4\sqrt{6}}{3}x as a single fraction.

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

To raise \frac{4\sqrt{6}x}{3} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{3^{2}}{3^{2}}.

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

Since \frac{x^{2}\times 3^{2}}{3^{2}} and \frac{\left(4\sqrt{6}x\right)^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

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

Expand \left(4\sqrt{6}x\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}+\frac{16\left(\sqrt{6}\right)^{2}x^{2}}{3^{2}}$$

The square of \sqrt{6} is 6.

$$x^{2}+\frac{16\times 6x^{2}}{3^{2}}$$

Multiply 16 and 6 to get 96.

$$x^{2}+\frac{96x^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+\frac{96x^{2}}{9}$$

Divide 96x^{2} by 9 to get \frac{32}{3}x^{2}.

$$x^{2}+\frac{32}{3}x^{2}$$

Combine x^{2} and \frac{32}{3}x^{2} to get \frac{35}{3}x^{2}.

$$\frac{35}{3}x^{2}$$

Expand

$$\frac{35x^{2}}{3}$$

Solution Steps

Express \frac{4\sqrt{6}}{3}x as a single fraction.

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

To raise \frac{4\sqrt{6}x}{3} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{3^{2}}{3^{2}}.

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

Since \frac{x^{2}\times 3^{2}}{3^{2}} and \frac{\left(4\sqrt{6}x\right)^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

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

Expand \left(4\sqrt{6}x\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}+\frac{16\left(\sqrt{6}\right)^{2}x^{2}}{3^{2}}$$

The square of \sqrt{6} is 6.

$$x^{2}+\frac{16\times 6x^{2}}{3^{2}}$$

Multiply 16 and 6 to get 96.

$$x^{2}+\frac{96x^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+\frac{96x^{2}}{9}$$

Divide 96x^{2} by 9 to get \frac{32}{3}x^{2}.

$$x^{2}+\frac{32}{3}x^{2}$$

Combine x^{2} and \frac{32}{3}x^{2} to get \frac{35}{3}x^{2}.

$$\frac{35}{3}x^{2}$$