Solve (m^2-1/2)*(m^2+1/2)

$$( m ^ { 2 } - 1 / 2 ) \cdot ( m ^ { 2 } + 1 / 2 )$$

Evaluate

$$m^{4}-\frac{1}{4}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square \frac{1}{2}.

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

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

$$m^{4}-\frac{1}{4}$$

Expand

$$m^{4}-\frac{1}{4}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square \frac{1}{2}.

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

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

$$m^{4}-\frac{1}{4}$$