Solve (m^6+1/3)*(m^6-1/3)

$$( m ^ { 6 } + 1 / 3 ) \cdot ( m ^ { 6 } - 1 / 3 )$$

Evaluate

$$m^{12}-\frac{1}{9}$$

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}{3}.

$$\left(m^{6}\right)^{2}-\frac{1}{9}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$m^{12}-\frac{1}{9}$$

Expand

$$m^{12}-\frac{1}{9}$$

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}{3}.

$$\left(m^{6}\right)^{2}-\frac{1}{9}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$m^{12}-\frac{1}{9}$$