Question

How do you factor `36m^3 - 6m^2 p^2 - 6mp + p^3`?

Answer 1

Grouping works well here. Notice that the ratio of the first coefficient to the second is `-6` and the ratio of the third coefficient to the fourth is also `-6`. So we find:

`36m^3-6m^2p^2-6mp+p^3`

`= (36m^3-6m^2p^2)-(6mp-p^3)`

`= 6m^2(6m-p^2)-p(6m-p^2)`

`= (6m^2-p)(6m-p^2)`