Cool Problem

Find the constant term in the expansion of $\Big(2z - \frac{1}{\sqrt{z}}\Big)^9$
 

 

Check out this problem! I was doing homework, and this was one of the problems!

 

The solution was pretty cool. also, do not scroll down if you don't want to see the answer. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANSWER: 

formula:

$\binom{9}{k} (2z)^{9-k}\Big(-\frac{1}{\sqrt{z}}\Big)^k = \binom{9}{k}(-1)^k 2^{9 - k} \frac{z^{9-k}}{z^{k/2}}.$

Answer:

$\binom{9}{6} (-1)^6 2^{9 - 6} = \boxed{672}$