I am to determine

by using Taylor expansion about

for

In our toolkit, we have

Now, plugging in the polynomial for

into the polynomial for

and then cubing(!!!) it all sounds not like something fun at all to do, but I have done similar problems for and that is really the best(?) way to go.

Do you guys have any tips for how I can make the polynomial multiplication easier and quickly obtain the sought coefficient, instead of having to really multiply out too many terms and add upp their coefficients etc.