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Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

 Mar 31, 2024
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To find the constant term in the expansion of the expression (2z - 1/√z) * 5 *(z - 1/√z)^3, we first need to expand the entire expression using the binomial theorem. Start by simplifying this equation to get a polynomial. However, we’re only interested in the constant term, so we’re looking for terms that won’t include z when multiplied together. We find these in the following multiplicands from each factor: -1/√z from (2z - 1/√z), and z^3 from (z - 1/√z)^3. When these are multiplied together, they result in a constant term.

So the answer is: \(-1/\sqrt{z} \) and \(z^3\)

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