Odpowiedź:
zad 1
a)
(3 + x)³ = 3³ + 3 * 3² * x + 3 * 3 * x² + x³ = 27 + 27x + 27x² + x³
b)
(2x - 4)³ = (2x)³ - 3 * (2x)² * 4 + 3 * 2x * 4³ - 4³ = 8x³ - 3 * 4x² * 4 + 6x * 64 - 64 =
= 8x³ - 48x² + 384x - 64
c)
(5 + 1/3x)³ = 5³ + 3 * 5² * 1/3x + 3 * 5 * (1/3x)² + (1/3x)³ =
= 125 + 3 * 25 * 1/3x + 15 * 1/9x² + 1/27x³ = 125 + 75 * 1/3x + 15/9x² + 1/27x³ =
= 125 + 75/3x + 5/3x² + 1/27x³ = 125 + 25x + 5/3x² + 1/27x³
d)
(3x - 3y)³ = (3x)³ - 3 * (3x)² * 3y + 3 * 3x * (3y)² - (3y)³ =
= 27x³ - 3 * 9x² * 3y + 6x * 9y² - 27y³ = 27x³ - 81x²y + 54xy² - 27y³
e)
(∛3x + ∛9)³ = (∛3x)³ + 3 * (∛3x)² * ∛9 + 3 * ∛3x * (∛9)² + (∛9)³ =
= 3x³ + 3 * ∛9 * x² * ∛9 + 3∛81 * x + 9 = 3x³ + 3∛9x² + 3 * ∛(27 * 3) * x + 9 =
= 3x³ + 3∛9x² + 3 * 3∛3 * x + 9 = 3x³ + 3∛9x² + 9∛3x + 9
f)
(- 4x - 10)³ = - (4x + 10)³ = - [(4x³) + 3 * (4x)² * 10 + 3 * 4x * 10² + 10³] =
= - ( 64x³ + 3 * 16x² * 10 + 12x * 100 + 1000) = - (64x³ + 480x² + 1200x + 1000) =
= - 64x³ - 480x² - 1200x - 1000
Szczegółowe wyjaśnienie:
wzory do obliczeń
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³
