Solve frac{sqrt{3}}{4}x(-3/2x+24)

$$\frac { \sqrt { 3 } } { 4 } x ( - \frac { 3 } { 2 } x + 24 )$$

Evaluate

$$\frac{3\sqrt{3}x\left(16-x\right)}{8}$$

Short Solution Steps

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

$$\frac{\sqrt{3}x}{4}\left(-\frac{3}{2}x+24\right)$$

Use the distributive property to multiply \frac{\sqrt{3}x}{4} by -\frac{3}{2}x+24.

$$\frac{\sqrt{3}x}{4}\left(-\frac{3}{2}\right)x+24\times \frac{\sqrt{3}x}{4}$$

Multiply \frac{\sqrt{3}x}{4} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{3}x\times 3}{4\times 2}x+24\times \frac{\sqrt{3}x}{4}$$

Express \frac{-\sqrt{3}x\times 3}{4\times 2}x as a single fraction.

$$\frac{-\sqrt{3}x\times 3x}{4\times 2}+24\times \frac{\sqrt{3}x}{4}$$

Cancel out 4, the greatest common factor in 24 and 4.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 6\sqrt{3}x times \frac{4\times 2}{4\times 2}.

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

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

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

Do the multiplications in -\sqrt{3}x\times 3x+6\sqrt{3}x\times 4\times 2.

$$\frac{-3\sqrt{3}x^{2}+48\sqrt{3}x}{4\times 2}$$

Expand 4\times 2.

$$\frac{-3\sqrt{3}x^{2}+48\sqrt{3}x}{8}$$

Factor

$$\frac{3\sqrt{3}x\left(16-x\right)}{8}$$