Let's determine the

$$
\begin{array}{r}
\text { a) }\left(\frac{x^{2}}{3}-\frac{3}{4 x}\right)^{7} \\
\text { and b) }\left(\frac{3 a}{2}+\frac{4 b}{3}\right)^{8}
\end{array}
$$

fourth and fifth terms, respectively, of their expansions.
a) According to the binomial theorem, the fourth term of the expansion is:

$$
\binom{7}{3}\left(\frac{x^{2}}{3}\right)^{4}\left(-\frac{3}{4 x}\right)^{3}=-\frac{7 \cdot 6 \cdot 5}{1 \cdot 2 \cdot 3} \cdot \frac{x^{8} \cdot 3^{3}}{3^{4} \cdot 4^{3} x^{3}}=-35 \cdot \frac{x^{5}}{3 \cdot 64}=-\frac{35 x^{5}}{192}
$$

b) The fifth term of the expansion is:

$$
\binom{8}{4}\left(\frac{3 a}{2}\right)^{4}\left(\frac{4 b}{3}\right)^{4}=\frac{8 \cdot 7 \cdot 6 \cdot 5}{1 \cdot 2 \cdot 3 \cdot 4} \cdot \frac{3^{4} a^{4} 2^{8} b^{4}}{2^{4} 3^{4}}=70 \cdot 2^{4} a^{4} b^{4}=1120 a^{4} b^{4}
$$

Lackner Györgyi (Bp. V. Textile and Industrial Technology I. o. t.)