I'm following a course on singular perturbation problems and finding the expansion of the solutions of equations depending on a parameter. In those problems I often have to expand brackets raised to powers and I wanted to know if there were any tricks to do it fast?
Example:
$$(x_0 + cx_1+c^2x_2 + O(c^3))^3$$
So here technically, I'm only concerned by writing down terms that are not $O(c^3)$.
Any ideas?
Many thanks!