3.71: Binomial expansion: coefficient and product of expansions

In the expansion of $\left(2k - \dfrac{x}{k}\right)^{5}$, where $k$ is a constant, the coefficient of $x^{2}$ is 160. Find the value of $k$.

Find, in ascending powers of $x$, the first 3 terms in the expansion of $(1 + 3x)^{6}$, simplifying the coefficient of each term.

When $(1 + 3x)^{6}(a + x)^{2}$ is written in ascending powers of $x$, the first three terms are $4 + 68x + bx^{2}$, where $a$ and $b$ are constants. Find the value of $a$ and of $b$.