# Binomial Theorem problem!

• January 19th 2010, 09:57 AM
Kakariki
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:
$[(8C4)(2a)^4(3a^{-2})^4)]$
$[(70)(16a^4)(81a^{-8})]$
$90720a^{-4}$

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

Wolfram alpha: http://www.wolframalpha.com/input/?i=%282a+%2B+%283a^%28-2%29%29%29^8
• January 19th 2010, 10:40 AM
Plato
It appears that the author of the textbook answer has a different interpretation of what “the first five terms” means.
The given answer is in ascending order of exponents.

Actually because of the vagueness of “the first five terms” the is no absolutely correct answer.