# How do you factor completely 81 x^4 - 256?

Aug 8, 2016

$\left(9 {x}^{2} + 16\right) \left(3 x + 4\right) \left(3 x - 4\right)$
${3}^{4} {x}^{4} - {16}^{2}$
=${\left(3 x\right)}^{4} - {16}^{2}$
=${\left(9 {x}^{2}\right)}^{2} - 16 {x}^{2}$
=$\left(9 {x}^{2} + 16\right) \left(9 {x}^{2} - 16\right)$
=$\left(9 {x}^{2} + 16\right) \left(3 x + 4\right) \left(3 x - 4\right)$