find the coefficient of $\large x^4 $ in the binomial of $\large (3-2x)^6 $

Question

mimi_x3 · Answer

Is in the expansion and binomial the same? lol

sasogeek · Answer

i believe so

sasogeek · Answer

here's what i'm getting though it's not in the possible answers...270
that being $$\ 15(3^2)\times 2 $$

anonymous · Answer

let evaluate this way: we know (n,k)=nCk

sasogeek · Answer

oh i see my mistake... i forgot to raise 2 to the power 4 too :) let's see if it get it :)

mimi_x3 · Answer

If yes, then..
$$\left(\begin{matrix}6 \ 4\end{matrix}\right)*(3)^{6-4}*(-2x)^4$$
$$15*3^2*16x^4$$
= $$2160x^4$$

sasogeek · Answer

yea 2160 is a possible solution :)

mimi_x3 · Answer

anonymous · Answer

also we know (a+b)^2=2C0a^2+2C1ab+2C2b^2 so do the same instead of power six go up to coef of 4

anonymous · Answer

mimi_x3 · Answer

Well, you can use  the formula, that i used that is easier i guess..