Solve (a+b)^2/4pi-a^2/4pi-b^2/4pi

$$\frac { ( a + b ) ^ { 2 } } { 4 } \pi - \frac { a ^ { 2 } } { 4 } \pi - \frac { b ^ { 2 } } { 4 } \pi$$

Evaluate

$$\frac{\pi ab}{2}$$

Short Solution Steps

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

$$\frac{\left(a+b\right)^{2}\pi }{4}-\frac{a^{2}}{4}\pi -\frac{b^{2}}{4}\pi$$

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

$$\frac{\left(a+b\right)^{2}\pi }{4}-\frac{a^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

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

$$\frac{\left(a+b\right)^{2}\pi -a^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

Do the multiplications in \left(a+b\right)^{2}\pi -a^{2}\pi .

$$\frac{a^{2}\pi +2ab\pi +b^{2}\pi -a^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

Combine like terms in a^{2}\pi +2ab\pi +b^{2}\pi -a^{2}\pi .

$$\frac{2ab\pi +b^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

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

$$\frac{2ab\pi +b^{2}\pi }{4}-\frac{b^{2}\pi }{4}$$

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

$$\frac{2ab\pi +b^{2}\pi -b^{2}\pi }{4}$$

Combine like terms in 2ab\pi +b^{2}\pi -b^{2}\pi .

$$\frac{2ab\pi }{4}$$

Divide 2ab\pi by 4 to get \frac{1}{2}ab\pi .

$$\frac{1}{2}ab\pi$$

Expand

$$\frac{\pi ab}{2}$$

Short Solution Steps

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

$$\frac{\left(a+b\right)^{2}\pi }{4}-\frac{a^{2}}{4}\pi -\frac{b^{2}}{4}\pi$$

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

$$\frac{\left(a+b\right)^{2}\pi }{4}-\frac{a^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

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

$$\frac{\left(a+b\right)^{2}\pi -a^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

Do the multiplications in \left(a+b\right)^{2}\pi -a^{2}\pi .

$$\frac{a^{2}\pi +2ab\pi +b^{2}\pi -a^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

Combine like terms in a^{2}\pi +2ab\pi +b^{2}\pi -a^{2}\pi .

$$\frac{2ab\pi +b^{2}\pi }{4}-\frac{b^{2}}{4}\pi$$

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

$$\frac{2ab\pi +b^{2}\pi }{4}-\frac{b^{2}\pi }{4}$$

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

$$\frac{2ab\pi +b^{2}\pi -b^{2}\pi }{4}$$

Combine like terms in 2ab\pi +b^{2}\pi -b^{2}\pi .

$$\frac{2ab\pi }{4}$$

Divide 2ab\pi by 4 to get \frac{1}{2}ab\pi .

$$\frac{1}{2}ab\pi$$