Solve 4pi-x^2/4pi-(4-x/2)^2pi

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

Evaluate

$$\frac{\pi x\left(4-x\right)}{2}$$

Short Solution Steps

Express \frac{x^{2}}{4}\pi as a single fraction.

$$4\pi -\frac{x^{2}\pi }{4}-\left(\frac{4-x}{2}\right)^{2}\pi$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4\pi times \frac{4}{4}.

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

Since \frac{4\times 4\pi }{4} and \frac{x^{2}\pi }{4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4\times 4\pi -x^{2}\pi .

$$\frac{16\pi -x^{2}\pi }{4}-\left(\frac{4-x}{2}\right)^{2}\pi$$

To raise \frac{4-x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{16\pi -x^{2}\pi }{4}-\frac{\left(4-x\right)^{2}}{2^{2}}\pi$$

Express \frac{\left(4-x\right)^{2}}{2^{2}}\pi as a single fraction.

$$\frac{16\pi -x^{2}\pi }{4}-\frac{\left(4-x\right)^{2}\pi }{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16\pi -x^{2}\pi }{4}-\frac{\left(4-x\right)^{2}\pi }{4}$$

Since \frac{16\pi -x^{2}\pi }{4} and \frac{\left(4-x\right)^{2}\pi }{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16\pi -x^{2}\pi -\left(4-x\right)^{2}\pi }{4}$$

Do the multiplications in 16\pi -x^{2}\pi -\left(4-x\right)^{2}\pi .

$$\frac{16\pi -x^{2}\pi -16\pi +8x\pi -x^{2}\pi }{4}$$

Combine like terms in 16\pi -x^{2}\pi -16\pi +8x\pi -x^{2}\pi .

$$\frac{-2x^{2}\pi +8x\pi }{4}$$

Expand

$$-\frac{\pi x^{2}}{2}+2\pi x$$

Short Solution Steps

Express \frac{x^{2}}{4}\pi as a single fraction.

$$4\pi -\frac{x^{2}\pi }{4}-\left(\frac{4-x}{2}\right)^{2}\pi$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4\pi times \frac{4}{4}.

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

Since \frac{4\times 4\pi }{4} and \frac{x^{2}\pi }{4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4\times 4\pi -x^{2}\pi .

$$\frac{16\pi -x^{2}\pi }{4}-\left(\frac{4-x}{2}\right)^{2}\pi$$

To raise \frac{4-x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{16\pi -x^{2}\pi }{4}-\frac{\left(4-x\right)^{2}}{2^{2}}\pi$$

Express \frac{\left(4-x\right)^{2}}{2^{2}}\pi as a single fraction.

$$\frac{16\pi -x^{2}\pi }{4}-\frac{\left(4-x\right)^{2}\pi }{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16\pi -x^{2}\pi }{4}-\frac{\left(4-x\right)^{2}\pi }{4}$$

Since \frac{16\pi -x^{2}\pi }{4} and \frac{\left(4-x\right)^{2}\pi }{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16\pi -x^{2}\pi -\left(4-x\right)^{2}\pi }{4}$$

Do the multiplications in 16\pi -x^{2}\pi -\left(4-x\right)^{2}\pi .

$$\frac{16\pi -x^{2}\pi -16\pi +8x\pi -x^{2}\pi }{4}$$

Combine like terms in 16\pi -x^{2}\pi -16\pi +8x\pi -x^{2}\pi .

$$\frac{-2x^{2}\pi +8x\pi }{4}$$