# How do you factor 27a^4 - a?

$a \left(3 a - 1\right) \left(9 {a}^{2} + 3 a + 1\right) .$
Formula : ${x}^{3} - {y}^{3} = \left(x - y\right) \left({x}^{2} + x y + {y}^{2}\right) .$
Expression $= 27 {a}^{4} - a = a \left(27 {a}^{3} - 1\right) = a \left\{{\left(3 a\right)}^{3} - {1}^{3}\right\} = a \left(3 a - 1\right) \left\{{\left(3 a\right)}^{2} + 3 a \cdot 1 + {1}^{2}\right\} = a \left(3 a - 1\right) \left(9 {a}^{2} + 3 a + 1\right) .$