Mathematics 9709/11 — October/November 2021

Expand $\left(1 - \frac{1}{2x}\right)^2$.

Find the first four terms in the expansion, in ascending powers of $x$, of $(1 + 2x)^6$.

Hence find the coefficient of $x$ in the expansion of $\left(1 - \frac{1}{2x}\right)^2 (1 + 2x)^6$.