Разложите многочлен на множители:
а) $\frac{1}{8}a^3 - \frac{8}{27}b^3$;
б) $\frac{64}{343}c^3 + \frac{729}{1000}d^3$;
в) $\frac{125}{512}x^3 - \frac{216}{343}y^3$;
г) $\frac{1}{729}m^3 + \frac{125}{216}n^3$.
$\frac{1}{8}a^3 - \frac{8}{27}b^3 = (\frac{1}{2}a)^3 - (\frac{2}{3}b)^3 = (\frac{1}{2}a - \frac{2}{3}b)((\frac{1}{2}a)^2 + \frac{1}{2}a * \frac{2}{3}b + (\frac{2}{3}b)^2) = (\frac{1}{2}a - \frac{2}{3}b)(\frac{1}{4}a^2 + \frac{1}{3}ab + \frac{4}{9}b^2)$
$\frac{64}{343}c^3 + \frac{729}{1000}d^3 = (\frac{4}{7}c)^3 + (\frac{9}{10}d)^3 = (\frac{4}{7}c + \frac{9}{10}d)((\frac{4}{7}c)^2 - \frac{4}{7}c * \frac{9}{10}d + (\frac{9}{10}d)^2) = (\frac{4}{7}c + \frac{9}{10}d)(\frac{16}{49}c^2 - \frac{2}{7}c * \frac{9}{5}d + \frac{81}{100}d^2) = (\frac{4}{7}c + \frac{9}{10}d)(\frac{16}{49}c^2 - \frac{18}{35}сd + \frac{81}{100}d^2)$
$\frac{125}{512}x^3 - \frac{216}{343}y^3 = (\frac{5}{8}x)^3 - (\frac{6}{7}y)^3 = (\frac{5}{8}x - \frac{6}{7}y)((\frac{5}{8}x)^2 + \frac{5}{8}x * \frac{6}{7}y + (\frac{6}{7}y)^2) = (\frac{5}{8}x - \frac{6}{7}y)(\frac{25}{64}x^2 + \frac{5}{4}x * \frac{3}{7}y + \frac{36}{49}y^2) = (\frac{5}{8}x - \frac{6}{7}y)(\frac{25}{64}x^2 + \frac{15}{28}xy + \frac{36}{49}y^2)$
$\frac{1}{729}m^3 + \frac{125}{216}n^3 = (\frac{1}{9}m)^3 + (\frac{5}{6}n)^3 = (\frac{1}{9}m + \frac{5}{6}n)((\frac{1}{9}m)^2 - \frac{1}{9}m * \frac{5}{6}n + (\frac{5}{6}n)^2) = (\frac{1}{9}m + \frac{5}{6}n)(\frac{1}{81}m^2 - \frac{5}{54}mn + \frac{25}{36}n^2)$
Пожауйста, оцените решение
