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 \( \Big(x^2+\frac{1}{x}\Big)^4\)
+23252 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.
