# How do you factor 10a^3-15a^2x-12ab^2+18b^3?

May 10, 2015

The $x$ factor in the second term is a bit troubling:

We could try:
$\textcolor{red}{10 {a}^{3} - 15 {a}^{2} x} - \textcolor{b l u e}{12 a {b}^{2} + 18 {b}^{3}}$

$= \textcolor{red}{\left(5 {a}^{2}\right) \left(2 a - 3 x\right)} - \textcolor{b l u e}{\left(6 {b}^{2}\right) \left(2 a - 3 b\right)}$

but since $\textcolor{red}{\left(2 x - 3 x\right)} \ne \textcolor{b l u e}{\left(2 a - 3 b\right)}$
we can't go much further.

(Note that other grouping run into the same problem)

If the $x$ was a typo and should have been a $b$
Then the completed factoring would be:
$\left(5 {a}^{2} - 6 {b}^{2}\right) \left(2 a - 3 b\right)$
... but "If wishes were horses..."