Разложите многочлен на множители:
а) $x^3y^3 - c^3$;
б) $m^6n^3 + p^{12}$;
в) $a^3 + m^3n^9$;
г) $q^3 - c^{15}d^{18}$.
$x^3y^3 - c^3 = (xy)^3 - c^3 = (xy - c)((xy)^2 + xyc + c^2) = (xy - c)(x^2y^2 + xyc + c^2)$
$m^6n^3 + p^{12} = (m^2n)^3 + (p^4)^3 = (m^2n + p^4)((m^2n)^2 - m^2np^4 + (p^4)^2) = (m^2n + p^4)(m^4n^2 - m^2np^4 + p^8)$
$a^3 + m^3n^9 = (a^3 + (mn^3)^3) = (a + mn^3)(a^2 - amn^3 + (mn^3)^2) = (a + mn^3)(a^2 - amn^3 + m^2n^6)$
$q^3 - c^{15}d^{18} = q^3 - (c^{5}d^{6})^3 = (q - c^5d^6)(q^2 + qc^5d^6 + (c^{5}d^{6})^2) = (q - c^5d^6)(q^2 + qc^5d^6 + c^{10}d^{12})$
Пожауйста, оцените решение
