Find the constant term in the expansion of \[\Big(2z - \frac{1}{\sqrt{z}}\Big)^9.\]
+36916 WolframAlpha says it is 84 ....but I do not know how to derive it ....Anyone?
+36916 Thanx , Heureka ! See answer below....turns out I entered it incorrectly in WA after all.... (transcribed as 'z' instead of '2z' .... D'Oh!)
+26367 Find the constant term in the expansion of \(\left(2z - \frac{1}{\sqrt{z}}\right)^9\).
\(\begin{array}{|rcll|} \hline && \dbinom{9}{6}*(2z)^3*\left(\frac{1}{\sqrt{z}}\right)^6 \\\\ &=& \dbinom{9}{6}*8z^3*\dfrac{1}{z^3} \\\\ &=& \dbinom{9}{6}*8\\\\ &=& \dbinom{9}{9-6}*8\\\\ &=& \dbinom{9}{3}*8\\\\ &=& \dfrac{9}{3}*\dfrac{8}{2}*\dfrac{7}{1}*8\\\\ &=& 3*4*7*8 \\\\ &=& 672 \\ \hline \end{array}\)
