Solve (mm-frac{1}2^2)^2

$$( m m - \frac { 1 } { 2 } ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{\left(4m^{2}-1\right)^{2}}{16}$$

Solution Steps

Multiply m and m to get m^{2}.

$$\left(m^{2}-\left(\frac{1}{2}\right)^{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\left(m^{2}-\frac{1}{4}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m^{2}-\frac{1}{4}\right)^{2}.

$$\left(m^{2}\right)^{2}-\frac{1}{2}m^{2}+\frac{1}{16}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{4}-\frac{1}{2}m^{2}+\frac{1}{16}$$

Expand

$$m^{4}-\frac{m^{2}}{2}+\frac{1}{16}$$

Solution Steps

Multiply m and m to get m^{2}.

$$\left(m^{2}-\left(\frac{1}{2}\right)^{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\left(m^{2}-\frac{1}{4}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m^{2}-\frac{1}{4}\right)^{2}.

$$\left(m^{2}\right)^{2}-\frac{1}{2}m^{2}+\frac{1}{16}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{4}-\frac{1}{2}m^{2}+\frac{1}{16}$$