Разложите многочлен на множители:
а) $\frac{1}{8}a^6 - b^9$;
б) $\frac{8}{27}a^3 + \frac{1}{64}x^9$;
в) $\frac{1}{125}x^3 + y^6$;
г) $\frac{64}{729}m^3 - \frac{343}{1000}n^6$.
$\frac{1}{8}a^6 - b^9 = (\frac{1}{2}a^2)^3 - (b^3)^3 = (\frac{1}{2}a^2 - b^3)((\frac{1}{2}a^2)^2 + \frac{1}{2}a^2b^3 + (b^3)^2) = (\frac{1}{2}a^2 - b^3)(\frac{1}{4}a^4 + \frac{1}{2}a^2b^3 + b^6)$
$\frac{8}{27}a^3 + \frac{1}{64}x^9 = (\frac{2}{3}a)^3 + (\frac{1}{4}x^3)^3 = (\frac{2}{3}a + \frac{1}{4}x^3)((\frac{2}{3}a)^2 - \frac{2}{3}a * \frac{1}{4}x^3 + (\frac{1}{4}x^3)^2) = (\frac{2}{3}a + \frac{1}{4}x^3)(\frac{4}{9}a^2 - \frac{1}{3}a * \frac{1}{2}x^3 + \frac{1}{16}x^6) = (\frac{2}{3}a + \frac{1}{4}x^3)(\frac{4}{9}a^2 - \frac{1}{6}ax^3 + \frac{1}{16}x^6)$
$\frac{1}{125}x^3 + y^6 = (\frac{1}{5}x)^3 + (y^2)^3 = (\frac{1}{5}x + y^2)((\frac{1}{5}x)^2 - \frac{1}{5}xy^2 + (y^2)^2) = (\frac{1}{5}x + y^2)(\frac{1}{25}x^2 - \frac{1}{5}xy^2 + y^4)$
$\frac{64}{729}m^3 - \frac{343}{1000}n^6 = (\frac{4}{9}m)^3 - (\frac{7}{10}n^2)^3 = (\frac{4}{9}m - \frac{7}{10}n^2)((\frac{4}{9}m)^2 + \frac{4}{9}m * \frac{7}{10}n^2 + (\frac{7}{10}n^2)^2) = (\frac{4}{9}m - \frac{7}{10}n^2)(\frac{16}{81}m^2 + \frac{2}{9}m * \frac{7}{5}n^2 + \frac{49}{100}n^4) = (\frac{4}{9}m - \frac{7}{10}n^2)(\frac{16}{81}m^2 + \frac{14}{45}mn^2 + \frac{49}{100}n^4)$
Пожауйста, оцените решение
