Question

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

Answer 1

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

We could try:
`color(red)(10a^3-15a^2x) - color(blue)(12ab^2+18b^3)`

`=color(red)((5a^2)(2a-3x)) - color(blue)((6b^2)(2a-3b))`

but since `color(red)((2x-3x))!=color(blue)((2a-3b))`
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:
`(5a^2-6b^2)(2a-3b)`
... but "If wishes were horses..."