Solve 108u^6+256v^6

$$108 u ^ { 6 } + 256 v ^ { 6 }$$

Factor

$$4\left(3u^{2}+4v^{2}\right)\left(9u^{4}-12u^{2}v^{2}+16v^{4}\right)$$

Solution Steps

Factor out 4.

$$4\left(27u^{6}+64v^{6}\right)$$

Consider 27u^{6}+64v^{6}. Rewrite 27u^{6}+64v^{6} as \left(3u^{2}\right)^{3}+\left(4v^{2}\right)^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(3u^{2}+4v^{2}\right)\left(9u^{4}-12u^{2}v^{2}+16v^{4}\right)$$

Rewrite the complete factored expression.

$$4\left(3u^{2}+4v^{2}\right)\left(9u^{4}-12u^{2}v^{2}+16v^{4}\right)$$

Evaluate

$$108u^{6}+256v^{6}$$