(a + b)^3 = a^3 + 3 a^2 b + 3 a b^2 + b^3 zatem (x + 4)^3 = x^3 + 3*x^2 *4 + 3*x*4^2 + 4^3 = = x^3 +12 x^2 + 48 x + 64 =========================== (1 - 2x)^3 = 1^3 - 3 *1^2 *(2x) + 3 *1*(2x)^2 - (2x)^3 = = 1 - 6x + 12 x^2 - 8 x^3 ======================== (x + 2)(x^2 -2x + 4) = x^3 - 2 x^2 + 4x + 2 x^2 - 4x + 8 = = x^3 + 8 ============ Równanie 2 x^3 + x^2 - 8x - 4 = 0 x^2 *( 2x + 1) - 4*(2x + 1) = 0 (x^2 - 4)*( 2x + 1) = 0 (x -2)*(x +2)*(2x + 1) = 0 x - 2 = 0 lub x + 2 = 0 lub 2x + 1 = 0 x = 2 lub x = - 2 lub 2x = - 1 x = 2 lub x = - 2 lub x = - 1/2 Odp. x1 = -2; x2 = - 1/2 , x3 = 2 ==================================
Wielomiany. Pomocnicze wzory skróconego mnożenia: (a+b)^3 = a^3 + 3a^2 *b + 3ab^2 + b^3 (a-b)^3 = a^3 - 3a^2 *b + 3ab^2 - b^3 a) (x+4)^3 = x^3 + 12x^2 + 48x + 64 b) (1-2x)^3 = 1 - 6x + 12x^2 - 8x^3 = -8x^3 + 12x^2 - 6x +1 c) (x+2)(x^2 - 2x + 4) = x^3 - 2x^2 + 4x + 2x^2 - 4x + 8 = x^3 + 8 Rozwiąż równanie. 2x^3 + x^2 - 8x - 4 = 0 x^2 *(2x+1) - 4(2x+1) = 0 (x^2 - 4)(2x+1) = 0 (x+2)(x-2)(2x+1) = 0 x = -2, v x = -1/2, v x = 2
