Solve pir^2-pi(4r/5)^2

$$\pi r ^ { 2 } - \pi ( \frac { 4 r } { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{9\pi r^{2}}{25}$$

Short Solution Steps

To raise \frac{4r}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\pi r^{2}-\pi \times \frac{\left(4r\right)^{2}}{5^{2}}$$

Express \pi \times \frac{\left(4r\right)^{2}}{5^{2}} as a single fraction.

$$\pi r^{2}-\frac{\pi \times \left(4r\right)^{2}}{5^{2}}$$

Expand \left(4r\right)^{2}.

$$\pi r^{2}-\frac{\pi \times 4^{2}r^{2}}{5^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\pi r^{2}-\frac{\pi \times 16r^{2}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\pi r^{2}-\frac{\pi \times 16r^{2}}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \pi r^{2} times \frac{25}{25}.

$$\frac{25\pi r^{2}}{25}-\frac{\pi \times 16r^{2}}{25}$$

Since \frac{25\pi r^{2}}{25} and \frac{\pi \times 16r^{2}}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25\pi r^{2}-\pi \times 16r^{2}}{25}$$

Do the multiplications in 25\pi r^{2}-\pi \times 16r^{2}.

$$\frac{25\pi r^{2}-16\pi r^{2}}{25}$$

Combine like terms in 25\pi r^{2}-16\pi r^{2}.

$$\frac{9\pi r^{2}}{25}$$

Expand

$$\frac{9\pi r^{2}}{25}$$

Short Solution Steps

To raise \frac{4r}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\pi r^{2}-\pi \times \frac{\left(4r\right)^{2}}{5^{2}}$$

Express \pi \times \frac{\left(4r\right)^{2}}{5^{2}} as a single fraction.

$$\pi r^{2}-\frac{\pi \times \left(4r\right)^{2}}{5^{2}}$$

Expand \left(4r\right)^{2}.

$$\pi r^{2}-\frac{\pi \times 4^{2}r^{2}}{5^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\pi r^{2}-\frac{\pi \times 16r^{2}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\pi r^{2}-\frac{\pi \times 16r^{2}}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \pi r^{2} times \frac{25}{25}.

$$\frac{25\pi r^{2}}{25}-\frac{\pi \times 16r^{2}}{25}$$

Since \frac{25\pi r^{2}}{25} and \frac{\pi \times 16r^{2}}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25\pi r^{2}-\pi \times 16r^{2}}{25}$$

Do the multiplications in 25\pi r^{2}-\pi \times 16r^{2}.

$$\frac{25\pi r^{2}-16\pi r^{2}}{25}$$

Combine like terms in 25\pi r^{2}-16\pi r^{2}.

$$\frac{9\pi r^{2}}{25}$$