3.68: Binomial expansion of $(1+3x)^7$ and independent term

Use the binomial theorem to expand $(1 + 3x)^{7}$ in ascending powers of $x$, as far as the term in $x^{3}$. Simplify each term.

Show that your expansion from part (i) gives the value of $1.03^{7}$ as $1.23$ to $2$ decimal places.

Find the term independent of $x$ in the expansion of $\left(x^{2} + \dfrac{2}{x}\right)^{15}$.