Разложите многочлен на множители:
а) $a(2a - b)(a + b) - 3a(a + b)^2$;
б) $m(3m + n^2)(m - n) + mn(m - n)^2$;
в) $5x^2(3x - 8) + 10x(3x - 8)^2$;
г) $6d^2(2d - 5)^2 - 12d^2(2d - 5)(d + 5)$.
$a(2a - b)(a + b) - 3a(a + b)^2 = a(a + b)(2a - b - 3(a + b)) = a(a + b)(2a - b - 3a - 3b) = a(a + b)(-a - 4b) = -a(a + b)(a + 4b)$
$m(3m + n^2)(m - n) + mn(m - n)^2 = m(m - n)(3m + n^2 + n(m - n)) = m(m - n)(3m + n^2 + mn - n^2) = m(m - n)(3m + mn) = m^2(m - n)(3 + n)$
$5x^2(3x - 8) + 10x(3x - 8)^2 = 5x(3x - 8)(x + 2(3x - 8)) = 5x(3x - 8)(x + 6x - 16) = 5x(3x - 8)(7x - 16)$
$6d^2(2d - 5)^2 - 12d^2(2d - 5)(d + 5) = 6d^2(2d - 5)(2d - 5 - 2(d + 5)) = 6d^2(2d - 5)(2d - 5 - 2d - 10) = 6d^2(2d - 5) * (-15) = -90d^2(2d - 5)$
Пожауйста, оцените решение
