# 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?

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?

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.

$\left( {x - 3} \right)^8 = \sum\limits_{k = 0}^8 { {8 \choose k} x^{8 - k} \left( { - 3} \right)^k }$ so $k = 3$ give the term.