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

2. Find the constant term in the expansion of  $$\Big(x^2+\frac{1}{x}\Big)^4$$

Aug 2, 2020

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I'll do number 2 as an example:

(x + 1/x)4  =  1·(x)4·(1/x)0 + 4·(x)3·(1/x)1 + 6·(x)2·(1/x)2 + 4·(x)1·(1/x)3 + 1·(x)0·(1/x)4

=  1·x4·1 + 4x3·(1/x) + 6x2·(1/x2) + 4x·(1/x3) + 1·1·(1/x4)

=  x4 + 4x2 + 6 + 4/x2 + 1/x4

To find the coefficients, either use Pascal's Triangle or the formula for combinations.

Aug 2, 2020