Разложите многочлен на множители:
а) $\frac{16}{49}p^2q - q^3$;
б) $2\frac{7}{9}a^3b - \frac{ab^3}{4}$;
в) $c^3 - \frac{25}{36}cd^2$;
г) $\frac{mn^5}{9} - 3\frac{1}{16}m^3n$.
$\frac{16}{49}p^2q - q^3 = q(\frac{16}{49}p^2 - q^2) = q(\frac{4}{7}p - q)(\frac{4}{7}p + q)$
$2\frac{7}{9}a^3b - \frac{ab^3}{4} = ab(2\frac{7}{9}a^2 - \frac{b^2}{4}) = ab(\frac{25}{9}a^2 - \frac{1}{4}b^2) = ab(\frac{5}{3}a - \frac{1}{2}b)(\frac{5}{3}a + \frac{1}{2}b) = ab(1\frac{2}{3}a - \frac{1}{2}b)(1\frac{2}{3}a + \frac{1}{2}b)$
$c^3 - \frac{25}{36}cd^2 = c(c^2 - \frac{25}{36}d^2) = c(c - \frac{5}{6}d)(c + \frac{5}{6}d)$
$\frac{mn^5}{9} - 3\frac{1}{16}m^3n = mn(\frac{n^4}{9} - 3\frac{1}{16}m^2) = mn(\frac{1}{9}n^4 - \frac{49}{16}m^2) = mn(\frac{1}{3}n^2 - \frac{7}{4}m)(\frac{1}{3}n^2 + \frac{7}{4}m) = mn(\frac{1}{3}n^2 - 1\frac{3}{4}m)(\frac{1}{3}n^2 + 1\frac{3}{4}m)$
Пожауйста, оцените решение
