Math Help - Binomial coefficient second question

1. Binomial coefficient second question

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.

2. 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.

3. Originally Posted by brumby_3
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
find the coefficient $x^4$ in $(3x-(1/x^2))^{22}$
$(3x-(1/x^2))^{22}= _{22}C_k.(3x)^k.(x^{-2})^{(22-k)}.(-1)^{(22-k)}$
now, you need to find the value of $k$ first.
$(x)^k.(x^{-2})^{(22-k)}=x^4$