Using standard series from the List of Formulae (MF27), expand $e^{-2x}\sqrt{1+3x}$ up to and incl

Question

Using standard series from the List of Formulae (MF27), expand $e^{-2x}\sqrt{1+3x}$ up to and including the term in $x^3$.[3]

Accepted Answer

$1-\frac{1}{2}x-\frac{17}{8}x^2+\frac{269}{48}x^3+\cdots$

Product of exponential and binomial series