Binomial coefficient second question

Jul 2008
212
2
So I'm doing find the coefficient of x^4 in (3x-(1/x^2))^22

I've done where a = 3x and b = 1/x^2

(22)
(K) (3x)^K (-1/x^2)^(22-K)

(22)
(K) (3^K) (x^K) (-1)^(22-K) x^-2(22-K) ----- I think this is where I've stuffed up

(22)
(K) (3^K) (-1)^(22-K).... not sure from here lol.

Please help! Would be appreciated.
 
Jun 2009
806
275
nth term in a binomial expansion (a+b)^n is given by

T(r+1) = nCr*a^(n-r)*b^r

= 22Cr*(3)^(22-r)*(x)^(22-r)*(-1)^r*(1/x^2)^r

Collect the terms containing x and simplify. Equate the power of x to 4 and find the value of r.
 
Nov 2009
63
14
So I'm doing find the coefficient of x^4 in (3x-(1/x^2))^{22}

I've done where a = 3x and b = 1/x^2
Please help! Would be appreciated.
find the coefficient \(\displaystyle x^4\) in\(\displaystyle (3x-(1/x^2))^{22}\)

\(\displaystyle (3x-(1/x^2))^{22}= _{22}C_k.(3x)^k.(x^{-2})^{(22-k)}.(-1)^{(22-k)}\)

now, you need to find the value of \(\displaystyle k\) first.
\(\displaystyle (x)^k.(x^{-2})^{(22-k)}=x^4\)



......hope it'll help........(Clapping)