Solve m^4-81n^4

$$m ^ { 4 } - 81 n ^ { 4 }$$

Factor

$$\left(m-3n\right)\left(m+3n\right)\left(m^{2}+9n^{2}\right)$$

Solution Steps

Rewrite m^{4}-81n^{4} as \left(m^{2}\right)^{2}-\left(9n^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m^{2}-9n^{2}\right)\left(m^{2}+9n^{2}\right)$$

Consider m^{2}-9n^{2}. Rewrite m^{2}-9n^{2} as m^{2}-\left(3n\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m-3n\right)\left(m+3n\right)$$

Rewrite the complete factored expression.

$$\left(m-3n\right)\left(m+3n\right)\left(m^{2}+9n^{2}\right)$$

Evaluate

$$m^{4}-81n^{4}$$