3. Найдите сумму, разность и произведение многочленов: $$\frac{7}{15}c^2 + \frac{5}{7}d^3; \quad \frac{3}{5}c^2 - \frac{10}{21}d^3$$.

Сумма: $$\frac{7}{15}c^2 + \frac{5}{7}d^3 + \frac{3}{5}c^2 - \frac{10}{21}d^3 = (\frac{7}{15} + \frac{3}{5})c^2 + (\frac{5}{7} - \frac{10}{21})d^3 = (\frac{7}{15} + \frac{9}{15})c^2 + (\frac{15}{21} - \frac{10}{21})d^3 = \frac{16}{15}c^2 + \frac{5}{21}d^3$$. Разность: $$\frac{7}{15}c^2 + \frac{5}{7}d^3 - (\frac{3}{5}c^2 - \frac{10}{21}d^3) = (\frac{7}{15} - \frac{3}{5})c^2 + (\frac{5}{7} + \frac{10}{21})d^3 = (\frac{7}{15} - \frac{9}{15})c^2 + (\frac{15}{21} + \frac{10}{21})d^3 = -\frac{2}{15}c^2 + \frac{25}{21}d^3$$. Произведение: $$(\frac{7}{15}c^2 + \frac{5}{7}d^3)(\frac{3}{5}c^2 - \frac{10}{21}d^3) = \frac{7}{15}c^2 \cdot \frac{3}{5}c^2 - \frac{7}{15}c^2 \cdot \frac{10}{21}d^3 + \frac{5}{7}d^3 \cdot \frac{3}{5}c^2 - \frac{5}{7}d^3 \cdot \frac{10}{21}d^3 = \frac{7 \cdot 3}{15 \cdot 5}c^4 - \frac{7 \cdot 10}{15 \cdot 21}c^2d^3 + \frac{5 \cdot 3}{7 \cdot 5}c^2d^3 - \frac{5 \cdot 10}{7 \cdot 21}d^6 = \frac{7}{25}c^4 - \frac{2}{9}c^2d^3 + \frac{3}{7}c^2d^3 - \frac{50}{147}d^6 = \frac{7}{25}c^4 + (\frac{3}{7} - \frac{2}{9})c^2d^3 - \frac{50}{147}d^6 = \frac{7}{25}c^4 + (\frac{27}{63} - \frac{14}{63})c^2d^3 - \frac{50}{147}d^6 = \frac{7}{25}c^4 + \frac{13}{63}c^2d^3 - \frac{50}{147}d^6.