Разложите многочлен на множители:
а) $x^3 - x^2y - xy^2 + y^3$;
б) $c^2 + 2c - d^2 + 2d$;
в) $a^3 + a^2b - ab^2 - b^3$;
г) $m^2 - 2n - m - 4n^2$.
$x^3 - x^2y - xy^2 + y^3 = (x^3 - x^2y) - (xy^2 - y^3) = x^2(x - y) - y^2(x - y) = (x - y)(x^2 - y^2) = (x - y)(x - y)(x + y) = (x - y)^2(x + y)$
$c^2 + 2c - d^2 + 2d = c^2 - d^2 + 2(c + d) = (c - d)(c + d) + 2(c + d) = (c + d)(c - d + 2)$
$a^3 + a^2b - ab^2 - b^3 = (a^3 - b^3) + (a^2b - ab^2) = (a - b)(a^2 + ab + b^2) + ab(a - b) = (a - b)(a^2 + ab + b^2 + ab) = (a - b)(a^2 + 2ab + b^2) = (a - b)(a + b)^2$
$m^2 - 2n - m - 4n^2 = (m^2 - 4n^2) - (2n + m) = (m - 2n)(m + 2n) - (m + 2n) = (m + 2n)(m - 2n - 1)$
Пожауйста, оцените решение
