# How do you factor 16ax^3 + 54ay^3?

Jun 7, 2015

$16 a {x}^{3} + 54 a {y}^{3}$

$= 2 a \left(8 {x}^{3} + 27 {y}^{3}\right)$

$= 2 a \left({\left(2 x\right)}^{3} + {\left(3 y\right)}^{3}\right)$

$= 2 a \left(2 x + 3 y\right) \left({\left(2 x\right)}^{2} - \left(2 x\right) \left(3 y\right) + {\left(3 y\right)}^{2}\right)$

$= 2 a \left(2 x + 3 y\right) \left(4 {x}^{2} - 6 x y + 9 {y}^{2}\right)$

...using the sum of cubes identity:

${A}^{3} + {B}^{3} = \left(A + B\right) \left({A}^{2} - A B + {B}^{2}\right)$

There are no simpler factors with real coefficients.