Solve 16m^8/625-256/81n^8

$$\frac { 16 m ^ { 8 } } { 625 } - \frac { 256 } { 81 } n ^ { 8 }$$

Factor

$$\frac{16\left(3m^{2}-10n^{2}\right)\left(3m^{2}+10n^{2}\right)\left(9m^{4}+100n^{4}\right)}{50625}$$

Solution Steps

Factor out \frac{16}{50625}.

$$\frac{16\left(81m^{8}-10000n^{8}\right)}{50625}$$

Consider 81m^{8}-10000n^{8}. Rewrite 81m^{8}-10000n^{8} as \left(9m^{4}\right)^{2}-\left(100n^{4}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9m^{4}-100n^{4}\right)\left(9m^{4}+100n^{4}\right)$$

Consider 9m^{4}-100n^{4}. Rewrite 9m^{4}-100n^{4} as \left(3m^{2}\right)^{2}-\left(10n^{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).

$$\left(3m^{2}-10n^{2}\right)\left(3m^{2}+10n^{2}\right)$$

Rewrite the complete factored expression.

$$\frac{16\left(3m^{2}-10n^{2}\right)\left(3m^{2}+10n^{2}\right)\left(9m^{4}+100n^{4}\right)}{50625}$$

Evaluate

$$\frac{16m^{8}}{625}-\frac{256n^{8}}{81}$$