Сократите дробь:
а) $\frac{16a^2 - 8ab + b^2}{64a^3 - b^3}$;
б) $\frac{8p^3 + 27q^3}{4p^2 + 12pq + 9q^2}$;
в) $\frac{125x^3 - y^3}{25x^2 - 10xy + y^2}$;
г) $\frac{27n^3 + 64m^3}{9n^2 + 24mn + 16m^2}$.
$\frac{16a^2 - 8ab + b^2}{64a^3 - b^3} = \frac{(4a - b)^2}{(4a - b)(16a^2 + 4ab + b^2)} = \frac{4a - b}{16a^2 + 4ab + b^2}$
$\frac{8p^3 + 27q^3}{4p^2 + 12pq + 9q^2} = \frac{(2p + 3q)(4p^2 - 6pq + 9q^2)}{(2p + 3q)^2} = \frac{4p^2 - 6pq + 9q^2}{2p + 3q}$
$\frac{125x^3 - y^3}{25x^2 - 10xy + y^2} = \frac{(5x - y)(25x^2 + 5xy + y^2)}{(5x - y)^2} = \frac{25x^2 + 5xy + y^2}{5x - y}$
$\frac{27n^3 + 64m^3}{9n^2 + 24mn + 16m^2} = \frac{(3n + 4m)(9n^2 - 12mn + 16m^2)}{(3n + 4m)^2} = \frac{9n^2 - 12mn + 16m^2}{3n + 4m}$
Пожауйста, оцените решение
