Solve 16m^5-mn^2

$$16 m ^ { 5 } - m n ^ { 2 }$$

Factor

$$m\left(4m^{2}-n\right)\left(4m^{2}+n\right)$$

Solution Steps

Factor out m.

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

Consider 16m^{4}-n^{2}. Rewrite 16m^{4}-n^{2} as \left(4m^{2}\right)^{2}-n^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4m^{2}-n\right)\left(4m^{2}+n\right)$$

Rewrite the complete factored expression.

$$m\left(4m^{2}-n\right)\left(4m^{2}+n\right)$$

Evaluate

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