+0

0
91
3

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

it is not 5376

May 3, 2022

#1
0

By the Binomial theorem, the constant term is C(9,2)*2^4 = 576.

May 3, 2022
#2
0

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
+9459
0

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