F.4 exponential function

Note : e^x = 1 + x + (x^2) / 2! + (x^3) / 3! + ........+ (x^n) / n! + .......
(3x + 2)^7 / e^(-3x)
= [(3x + 2)^7] e^3x
= [(3x + 2)^7] [1 + 3x + (9x^2) / 2! + (27x^3) / 3! + ........+ ((3x)^n) / n! + .....]
= [2^7 + 7(2^6)(3x) + 7C2 (2^5)(9x^2) + ... + (3x)^7] *
[1 + 3x + (9x^2) / 2! + (27x^3) / 3! + ........+ ((3x)^n) / n! + .....]
= (128 + 1344x + 6048x^2 + ...)(1 + 3x + (9/2)x^2 + ...)
= 128 + 384x + 576x^2 + 1344x + 4032x^2 + 6048x^2 + ...
= 128 + 1728x + 10656x^2 + ...