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\[(x + \frac{k}{x})^7\]
\[(1 - 5x^2)(x + \frac{k}{x})^7\]

for first one, did you solve
\[35k^3=21k^2\]?

No, I'm completely at a lost here. Sorry. :(

because in general the terms of
\[(a+b)^n\] look like
\[\dbinom{n}{j}a^jb^{n-j}\]

let me know if this makes any sense, if not i will try again.

I'm sorry, but how did you get 2j - 7 = 1? D:

ok with that?
that is also why i set it equal to 3

since presumably
\[k\neq 0\] the only solution is
\[\frac{27}{35}\]

27?
\

oops

\[\frac{21}{35}\]looks more like it

maybe even
\[\frac{3}{5}\]

ick. your math teacher must hate you

No use expanding it the whole way, anyway. :))
You have no idea. Gave me 3 sets of these questions.

damn i screwed up somehow. first answer is right, but this one i messed up

I am... I'm sorry, but that totally confused me.

oh duh, it is
\[\dbinom{7}{6}\times \frac{3}{5}=7\times \frac{3}{5}=\frac{21}{5}\]

the second part of the problem is this
\[(1-5x^2)(x+\frac{k}{x})^7.\] right?

and you want the coefficient of the term
\[x^7\]

NONONO. I think I'd be able to do it. D: I really want to try it out by myself.

:)) Swear I will. A million thanks to you.