(a) To expand \((3 - 2x)^5\), use the binomial theorem:

\((3 - 2x)^5 = \sum_{k=0}^{5} \binom{5}{k} (3)^{5-k} (-2x)^k\).

The first three terms are:

\(\binom{5}{0} (3)^5 (-2x)^0 = 243\)

\(\binom{5}{1} (3)^4 (-2x)^1 = -810x\)

\(\binom{5}{2} (3)^3 (-2x)^2 = 1080x^2\)

Thus, the first three terms are \(243 - 810x + 1080x^2\).

(b) Expand \((4 + x)^2\):

\((4 + x)^2 = 16 + 8x + x^2\).

To find the coefficient of \(x^2\) in \((4 + x)^2(3 - 2x)^5\), consider:

\(16 \times 1080 + 8 \times (-810) + 243\).

Calculate:

\(16 \times 1080 = 17280\)

\(8 \times (-810) = -6480\)

\(17280 - 6480 + 243 = 11043\)

Thus, the coefficient of \(x^2\) is 11043.