+0  
 
0
72
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Find the constant term in the expansion of \[\Big(2z - \frac{1}{\sqrt{z}}\Big)^9.\]

 Aug 12, 2021
 #1
avatar+34374 
0

WolframAlpha says it is 84     ....but I do not know how to derive it ....Anyone?

 Aug 12, 2021
 #3
avatar+34374 
0

Thanx , Heureka !        See answer below....turns out I entered it incorrectly in WA after all.... (transcribed as 'z'  instead of '2z' .... D'Oh!)

ElectricPavlov  Aug 12, 2021
 #2
avatar+26213 
+1

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

 

\(\begin{array}{|rcll|} \hline && \dbinom{9}{6}*(2z)^3*\left(\frac{1}{\sqrt{z}}\right)^6 \\\\ &=& \dbinom{9}{6}*8z^3*\dfrac{1}{z^3} \\\\ &=& \dbinom{9}{6}*8\\\\ &=& \dbinom{9}{9-6}*8\\\\ &=& \dbinom{9}{3}*8\\\\ &=& \dfrac{9}{3}*\dfrac{8}{2}*\dfrac{7}{1}*8\\\\ &=& 3*4*7*8 \\\\ &=& 672 \\ \hline \end{array}\)

 

laugh

 Aug 12, 2021

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