Q:

Find the term for $x^3$ in $(3x+4)(x-2)^4$

I'm sure there's an algebraic trick to it using the binomial theorem/Pascal's triangle, but I can't think of it right now. How do I get to the solution without manually expanding everything?

A:

Hint:
$$(x-2)^4 = \sum_{i=0}^4 \binom4i x^i(-2)^{4-i}$$
Don't compute everything, just extract what you need from this formula.

