Solve 216m^6-27n^6

$$216 m ^ { 6 } - 27 n ^ { 6 }$$

Factor

$$27\left(2m^{2}-n^{2}\right)\left(4m^{4}+2m^{2}n^{2}+n^{4}\right)$$

Solution Steps

Factor out 27.

$$27\left(8m^{6}-n^{6}\right)$$

Consider 8m^{6}-n^{6}. Rewrite 8m^{6}-n^{6} as \left(2m^{2}\right)^{3}-\left(n^{2}\right)^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

Rewrite the complete factored expression.

$$27\left(2m^{2}-n^{2}\right)\left(4m^{4}+2m^{2}n^{2}+n^{4}\right)$$

Evaluate

$$216m^{6}-27n^{6}$$