Solve frac{sqrt{3}}{3}x^2+2sqrt{3}x

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

Evaluate

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

Short Solution Steps

Express \frac{\sqrt{3}}{3}x^{2} as a single fraction.

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

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

$$\frac{\sqrt{3}x^{2}}{3}+\frac{3\times 2\sqrt{3}x}{3}$$

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

$$\frac{\sqrt{3}x^{2}+3\times 2\sqrt{3}x}{3}$$

Do the multiplications in \sqrt{3}x^{2}+3\times 2\sqrt{3}x.

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

Factor

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

Solution Steps

Factor out \frac{1}{3}.

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

Consider \sqrt{3}x^{2}+6\sqrt{3}x. Factor out \sqrt{3}x.

$$\sqrt{3}x\left(x+6\right)$$

Rewrite the complete factored expression.

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