(a) To expand \((2 + 3x)^4\), use the binomial theorem:

\((2 + 3x)^4 = \sum_{k=0}^{4} \binom{4}{k} (2)^{4-k} (3x)^k\).

The first three terms are:

\(\binom{4}{0} (2)^4 (3x)^0 = 16\),

\(\binom{4}{1} (2)^3 (3x)^1 = 96x\),

\(\binom{4}{2} (2)^2 (3x)^2 = 216x^2\).

Thus, the first three terms are \(16 + 96x + 216x^2\).

(b) To expand \((1 - 2x)^5\), use the binomial theorem:

\((1 - 2x)^5 = \sum_{k=0}^{5} \binom{5}{k} (1)^{5-k} (-2x)^k\).

The first three terms are:

\(\binom{5}{0} (1)^5 (-2x)^0 = 1\),

\(\binom{5}{1} (1)^4 (-2x)^1 = -10x\),

\(\binom{5}{2} (1)^3 (-2x)^2 = 40x^2\).

Thus, the first three terms are \(1 - 10x + 40x^2\).

(c) To find the coefficient of \(x^2\) in \((2 + 3x)^4 (1 - 2x)^5\), consider the products that result in \(x^2\):

\((16)(40) - (10)(96) + (1)(216)\).

Calculate:

\(640 - 960 + 216 = -104\).

Thus, the coefficient of \(x^2\) is \(-104\).