# Math Help - binomial theorem

1. ## binomial theorem

Find the 4th term of (x-3)8 (to the 8th power).

This is all I have for the question. Is this enough info to work this problem?

Thanks in advance.
Chu

2. Originally Posted by chu
Find the 4th term of (x-3)8 (to the 8th power).

This is all I have for the question. Is this enough info to work this problem?

Thanks in advance.
Chu
Not quite .....

The (r+1)th term (going in increasing powers of x) is $^8 C_r \, x^r (-3)^{8-r}$.

The (r+1)th term (going in decreasing powers of x) is $^8 C_r \, (-3)^r x^{8-r}$.

The answer will depend on which way you do it.

3. ## More info

I have more info now: problem with multiple choice answers. I'm still not sure A, B, C, D. Thanks Flow Master

4. There is a debate as to how one numbers the terms in a binominal expansion.
So much so, that in the US we have pretty much agreed not to use that terminology in contest questions.

But given you options, it is clear that Mr.F is correct you need to use the descending option.
$\left( {x - 3} \right)^8 = \sum\limits_{k = 0}^8 { {8 \choose k} x^{8 - k} \left( { - 3} \right)^k }$ so $k = 3$ give the term.
So the answer is either a or b.