# How do you factor 1029yx^3 + 24y^4?

May 12, 2015

$1029 y {x}^{3} + 24 {y}^{4} = 3 y \left(343 {x}^{3} + 8 {y}^{3}\right)$

$= 3 y \left({\left(7 x\right)}^{3} + {\left(2 y\right)}^{3}\right)$

$= 3 y \left(7 x + 2 y\right) \left({\left(7 x\right)}^{2} - \left(7 x\right) \left(2 y\right) + {\left(2 y\right)}^{2}\right)$

$= 3 y \left(7 x + 2 y\right) \left(49 {x}^{2} - 14 x y + 4 {y}^{2}\right)$

using ${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$

There are linear factors of $\left(49 {x}^{2} - 14 x y + 2 {y}^{2}\right)$, but they have Complex coefficients.