I must "use the binomial theorem to determine the coefficient x^14 in the expansion of (3x^2-1/3)^16".
I find that:
a=3x^2 (I believe)
I write that (sorry but the matrix brackets I cannot make):
(16) (3x^2) ^(16-14+1) (-1/3)^13
= (16) (3x^2)^3 (-1/3)^13
= (16!/(16-13)!13!) (1/? x^6)
This part is how I am getting confused.
Can somebody help me please to continue to solving this question? I must "expressing the coefficient as a fraction in lowest terms" but I don't think I have calculated well above to make the fraction to continue. The book is not showing this kind of difficult examples before we must do the assignment!
Tthank you for the replies.
I am following all of the details of your work but I am not understanding how you can be making a different formula to my formula.
I have the binomial formula from class (sorry I cannot make the brackets):
(n) * a^(n-r+1) * b^(r-1)
But your formula is :
(n) * a^(n-r) * b^r
Please is this formulas the same things?
Perhaps this is the reason why I am not making the same answer when I am working the problem?
I will appreciate it if you can be telling how this is the same.