Problem

(a) Give the complete expansion of $\bigg(x + \frac{2}{x}\bigg)^5$.

(b) In the expansion of $(a + bx^2)\bigg(x + \frac{2}{x}\bigg)^5$, the coefficient of $x$ is zero and the coefficient of $\frac{1}{x}$ is $80$.

Find the values of the constants $a$ and $b$.