Разложите двучлен на множители:
а) $m^3 - 1$;
б) $p^3 - 27q^3$;
в) $125x^3 - 8y^3$;
г) $64a^3 + 1000b^3$;
д) $x^6 - y^6$;
е) $m^{12} - 64$;
ж) $x^9 - x^6$;
з) $c^6d^3 - k^3$.
$m^3 - 1 = (m - 1)(m^2 + m + 1)$
$p^3 - 27q^3 = p^3 - (3q)^3 = (p - 3q)(p^2 + 3pq + (3q)^2) = (p - 3q)(p^2 + 3pq + 9q^2)$
$125x^3 - 8y^3 = (5x)^3 - (2y)^3 = (5x - 2y)((5x)^2 + 5x * 2y + (2y)^2) = (5x - 2y)(25x^2 + 10xy + 4y^2)$
$64a^3 + 1000b^3 = (4a)^3 + (10b)^3 = (4a + 10b)((4a)^2 - 4a * 10b + (10b)^2) = (4a + 10b)(16a^2 - 40ab + 100b^2)$
$x^6 - y^6 = (x^2)^3 - (y^2)^3 = (x - y)((x^2)^2 + x^2y^2 + (y^2)^2) = (x^2 - y^2)(x^4 + x^2y^2 + y^4)$
$m^{12} - 64 = (m^4)^3 - 4^3 = (m^4 - 4)((m^4)^2 + 4m^4 + 4^2) = (m^4 - 4)(m^8 + 4m^4 + 16)$
$x^9 - x^6 = (x^3)^3 - (x^2)^3 = (x^3 - x^2)((x^3)^2 + x^3 * x^2 + (x^2)^2) = (x^3 - x^2)(x^6 + x^5 + x^4) = x^2(x - 1)x^4(x^2 + x + 1) = x^6(x - 1)(x^2 + x + 1)$
$c^6d^3 - k^3 = (c^2d)^3 - k^3 = (c^2d - k)((c^2d)^2 + c^2dk + k^2) = (c^2d - k)(c^4d^2 + c^2dk + k^2)$
Пожауйста, оцените решение