# Math Help - Factorials, find the 58th term

1. ## Factorials, find the 58th term

find the 58th term in the expansion of (2x-3y)^100

2. ## The binomial theorem...

Originally Posted by cm3pyro
find the 58th term in the expansion of (2x-3y)^100
we will need this formula
${n\choose k}=\frac{n!}{k!(n-k)!}$

From the Binomial Therom this will generate the k+1 th term.

${{n}\choose {k}}a^{n-k}b^k$

so we need n=100 k=57
$a=2x$ and $b=-3y$

evaluating at the above values gives

${{n}\choose {k}}a^{n-k}b^k=\frac{100!}{57!(100-57)!}(2x)^{100-57}(-3y)^{57}$

I hope this helps

3. (-3)^57

(-3y)^57, correct?

4. Yes sorry for the typo.