Solve 64m^3-mn^2

$$64 m ^ { 3 } - m n ^ { 2 }$$

Factor

$$m\left(8m-n\right)\left(8m+n\right)$$

Solution Steps

Factor out m.

$$m\left(64m^{2}-n^{2}\right)$$

Consider 64m^{2}-n^{2}. Rewrite 64m^{2}-n^{2} as \left(8m\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).

$$\left(8m-n\right)\left(8m+n\right)$$

Rewrite the complete factored expression.

$$m\left(8m-n\right)\left(8m+n\right)$$

Evaluate

$$m\left(64m^{2}-n^{2}\right)$$