I was asked to multiply these two power series expansions: ie. $p(x)q(x)$
$$p(x) = 2(x − 4) − 7(x − 4)^2 + 5(x − 4)^3 + . . .$$
$$q(x) = 4 − 3(x − 4) + (x − 4)^3 + . . .$$
and I was wondering if there's a trick to doing this without distributing and multiplying everything out before adding "like terms". Thank you!