Solve pih^2/2+5h-pih^2

$$\frac { \pi h ^ { 2 } } { 2 } + 5 h - \pi h ^ { 2 }$$

Evaluate

$$\frac{h\left(10-\pi h\right)}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5h times \frac{2}{2}.

$$\frac{\pi h^{2}}{2}+\frac{2\times 5h}{2}-\pi h^{2}$$

Since \frac{\pi h^{2}}{2} and \frac{2\times 5h}{2} have the same denominator, add them by adding their numerators.

$$\frac{\pi h^{2}+2\times 5h}{2}-\pi h^{2}$$

Do the multiplications in \pi h^{2}+2\times 5h.

$$\frac{\pi h^{2}+10h}{2}-\pi h^{2}$$

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

$$\frac{\pi h^{2}+10h}{2}-\frac{2\pi h^{2}}{2}$$

Since \frac{\pi h^{2}+10h}{2} and \frac{2\pi h^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\pi h^{2}+10h-2\pi h^{2}}{2}$$

Combine like terms in \pi h^{2}+10h-2\pi h^{2}.

$$\frac{-\pi h^{2}+10h}{2}$$

Factor

$$\frac{h\left(10-\pi h\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{\pi h^{2}+10h-2\pi h^{2}}{2}$$

Consider \pi h^{2}+10h-2\pi h^{2}. Factor out h.

$$h\left(\pi h+10-2\pi h\right)$$

Rewrite the complete factored expression.

$$\frac{h\left(\pi h+10-2\pi h\right)}{2}$$