Solve (a/2)^2*pidiv2-(a/2div2)^2*pidiv2

$$( \frac { a } { 2 } ) ^ { 2 } \cdot \pi \div 2 - ( \frac { a } { 2 } \div 2 ) ^ { 2 } \cdot \pi \div 2$$

Evaluate

$$\frac{3\pi a^{2}}{32}$$

Solution Steps

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{a^{2}\pi }{2^{3}}-\frac{\left(\frac{\frac{a}{2}}{2}\right)^{2}\pi }{2}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{a^{2}\pi }{8}-\frac{\left(\frac{\frac{a}{2}}{2}\right)^{2}\pi }{2}$$

Express \frac{\frac{a}{2}}{2} as a single fraction.

$$\frac{a^{2}\pi }{8}-\frac{\left(\frac{a}{2\times 2}\right)^{2}\pi }{2}$$

Multiply 2 and 2 to get 4.

$$\frac{a^{2}\pi }{8}-\frac{\left(\frac{a}{4}\right)^{2}\pi }{2}$$

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

$$\frac{a^{2}\pi }{8}-\frac{\frac{a^{2}}{4^{2}}\pi }{2}$$

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

$$\frac{a^{2}\pi }{8}-\frac{\frac{a^{2}\pi }{4^{2}}}{2}$$

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

$$\frac{a^{2}\pi }{8}-\frac{a^{2}\pi }{4^{2}\times 2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{a^{2}\pi }{8}-\frac{a^{2}\pi }{16\times 2}$$

Multiply 16 and 2 to get 32.

$$\frac{a^{2}\pi }{8}-\frac{a^{2}\pi }{32}$$

Combine \frac{a^{2}\pi }{8} and -\frac{a^{2}\pi }{32} to get \frac{3}{32}a^{2}\pi .

$$\frac{3}{32}a^{2}\pi$$

Expand

$$\frac{3\pi a^{2}}{32}$$

Solution Steps

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{a^{2}\pi }{2^{3}}-\frac{\left(\frac{\frac{a}{2}}{2}\right)^{2}\pi }{2}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{a^{2}\pi }{8}-\frac{\left(\frac{\frac{a}{2}}{2}\right)^{2}\pi }{2}$$

Express \frac{\frac{a}{2}}{2} as a single fraction.

$$\frac{a^{2}\pi }{8}-\frac{\left(\frac{a}{2\times 2}\right)^{2}\pi }{2}$$

Multiply 2 and 2 to get 4.

$$\frac{a^{2}\pi }{8}-\frac{\left(\frac{a}{4}\right)^{2}\pi }{2}$$

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

$$\frac{a^{2}\pi }{8}-\frac{\frac{a^{2}}{4^{2}}\pi }{2}$$

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

$$\frac{a^{2}\pi }{8}-\frac{\frac{a^{2}\pi }{4^{2}}}{2}$$

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

$$\frac{a^{2}\pi }{8}-\frac{a^{2}\pi }{4^{2}\times 2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{a^{2}\pi }{8}-\frac{a^{2}\pi }{16\times 2}$$

Multiply 16 and 2 to get 32.

$$\frac{a^{2}\pi }{8}-\frac{a^{2}\pi }{32}$$

Combine \frac{a^{2}\pi }{8} and -\frac{a^{2}\pi }{32} to get \frac{3}{32}a^{2}\pi .

$$\frac{3}{32}a^{2}\pi$$