Сократите дробь:
а) $\frac{(a^2 - b^2)^2}{a^2 + 2ab + b^2}$;
б) $\frac{7x^2y^2 - 14xy^3 + 7y^4}{x^4 - 2x^2y^2 + y^4}$;
в) $\frac{p^2 - 2pq + q^2}{(q^2 - p^2)^2}$;
г) $\frac{m^4 - 2m^2n^2 + n^4}{6m^3n + 12m^2n^2 + 6n^3m}$.
$\frac{(a^2 - b^2)^2}{a^2 + 2ab + b^2} = \frac{((a - b)(a + b))^2}{(a + b)^2} = \frac{(a - b)^2(a + b)^2}{(a + b)^2} = (a - b)^2$
$\frac{7x^2y^2 - 14xy^3 + 7y^4}{x^4 - 2x^2y^2 + y^4} = \frac{7y^2(x^2 - 2xy + y^2)}{(x^2 - y^2)^2} = \frac{7y^2(x - y)^2}{((x - y)(x + y))^2} = \frac{7y^2(x - y)^2}{(x - y)^2(x + y)^2} = \frac{7y^2}{(x + y)^2}$
$\frac{p^2 - 2pq + q^2}{(q^2 - p^2)^2} = \frac{(p - q)^2}{(p^2 - q^2)^2} = \frac{(p - q)^2}{((p - q)(p + q))^2} = \frac{(p - q)^2}{(p - q)^2(p + q)^2} = \frac{1}{(p + q)^2}$
$\frac{m^4 - 2m^2n^2 + n^4}{6m^3n + 12m^2n^2 + 6n^3m} = \frac{(m^2 - n^2)^2}{6mn(m^2 + 2mn + n^2)} = \frac{((m - n)(m + n))^2}{6mn(m + n)^2} = \frac{(m - n)^2(m + n)^2}{6mn(m + n)^2} = \frac{(m - n)^2}{6mn}$
Пожауйста, оцените решение
