# Math Help - Binomial Theorem problem!

1. ## Binomial Theorem problem!

Hey,
Doing homework, and came across this question. I cannot for the life of me figure out what I am doing wrong, but it doesn't match up to the answer at the back of the book. It does on wolfram alpha. So am I doing this correctly?
Question:
Find the first five terms in the expansion of each of the following:
b) $(2a + 3a^{-2})^8$

My attempted answer: ***I do not know how to show combinations using Latex, so hopefully this makes sense. Example: $(8C0)$ is "8 choose 0"***
First Term:
$[(8C0)(2a)^8(3a^{-2})^0]$
$= [(1)(256a^8)(1)]$
$= 256a^8$

Second Term:
$[(8C1)(2a)^7(3a^{-2})^1]$
$= [(8)(128a^7)(3a^{-2})]$
$= 3072a^5$

Third Term:
$[(8C2)(2a)^6(3a^{-2})^2]$
$= [(28)(64a^6)(9a^{-4})]$
$= 16128a^2$

Fourth Term:
$[(8C3)(2a)^5(3a^{-2})^3)$
$= [(56)(32a^5)(27a^{-6})$
$= 48384a^{-1}$

Fifth Term:
$[(8C4)(2a)^4(3a^{-2})^4)]$
$[(70)(16a^4)(81a^{-8})]$
$90720a^{-4}$

$256a^{-8} + 3072a^{-9} + 16128a^{-10} + 48384a^{-11} + 90720a^{-12} +...$