Solve 2rpi-frac{3sqrt{3}r^2}{2}

$$2 r \pi - \frac { 3 \sqrt { 3 } r ^ { 2 } } { 2 }$$

Evaluate

$$\frac{r\left(-3\sqrt{3}r+4\pi \right)}{2}$$

Short Solution Steps

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

$$\frac{2\times 2r\pi }{2}-\frac{3\sqrt{3}r^{2}}{2}$$

Since \frac{2\times 2r\pi }{2} and \frac{3\sqrt{3}r^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2r\pi -3\sqrt{3}r^{2}}{2}$$

Do the multiplications in 2\times 2r\pi -3\sqrt{3}r^{2}.

$$\frac{4r\pi -3\sqrt{3}r^{2}}{2}$$

Factor

$$\frac{r\left(-3\sqrt{3}r+4\pi \right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{4r\pi -3\sqrt{3}r^{2}}{2}$$

Consider 4r\pi -3\sqrt{3}r^{2}. Factor out r.

$$r\left(4\pi -3\sqrt{3}r\right)$$

Rewrite the complete factored expression.

$$\frac{r\left(4\pi -3\sqrt{3}r\right)}{2}$$