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Find the constant term in the expansion of
(2z - 1/sqrtz)^9

 

it is not 5376

 May 3, 2022
 #1
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By the Binomial theorem, the constant term is C(9,2)*2^4 = 576.

 May 3, 2022
 #2
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Exapand  (2z - 1/sqrt(z))^9  

 

-5376 z^(9/2) - 1/z^(9/2) - 2016 z^(3/2) - 144/z^(3/2) - 2304 z^(15/2) + 512 z^9 + 4608 z^6 + 4032 z^3 + 18/z^3 + 672
The constant term is 672

 May 3, 2022
 #3
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Constant term is \(\displaystyle \binom{9}3 (2z)^3 \left(-\dfrac1{\sqrt z}\right)^6\). You can simplify this to get the constant term 672.

 May 3, 2022

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