Question

Binomial theroem

Answer 1

Determine the term independent of a in the expansion
\[\huge (\frac{ a+1 }{ a^{2/3} - a^{1/3} +1 }- \frac{ a-1 }{ a-a^{1/2} })^{10}\]

Answer 2

Ok so what does that mean? `term independent of a`

Answer 3

constant

Answer 4

Thanks dan -.-

Answer 5

a term which does not have "a" in it @iambatman ie. a constant

Answer 6

ah this qn is not cute

Answer 7

Ok so can we get a general term here?

Answer 8

first we need to simplify , if it does

Answer 9

It should be able to, but it's ugly haha, can we just use wolfram?

Answer 10

\[(\frac{ a+1 }{ a^{2/3} - a^{1/3} +1 }- \frac{ a-1 }{ a-a^{1/2} })^{10} = \frac{ (a^{5/6}-1)^{10} }{ a^5 }\]

Answer 11

@iambatman has done most of the job here. Just find the \(a^5\) term in the expansion of \((a^{5/6} - 1)^{10}\).

Answer 12

yes thank you very much @iambatman @owlfred