I think you need to use binomial theorem

Find the constant term in the expansion of (2z - 1/(z*sqrt(z)) + 1)^4.

Guest Apr 26, 2023

#1**+1 **

To get a constant term, we need the z's to cancel out. Notice that we can't eliminate the z with less than 4 \(2z\)'s and \({1 \over z \sqrt z}\)'s. The closest we can do is \((2z)^3 \times ({1 \over z \sqrt z})^2\), but that uses 5, so it doesn't work.

Thus, the only constant term will be the 1 multiplied by itself 4 times, which is \(1^4 = \color{brown}\boxed{1}\)

BuilderBoi Apr 26, 2023