Question

Calcule: (x+1).(x-2).(x-3)

Answer 1

(x+1).(x-2).(x-3) = 
(x² + x - 2x - 2) (x-3) = 
(x² - x -2) ( x -3) = 
x³ - x²+-2x - 3x² + 3x + 6 =
x³ - 4x² + x + 6

Answer 2

(x + 1) . (x - 2) . (x - 3)

(x + 1) . (x² - 5x + 6)

x³ + x² - 5x . x - 5x.1 + 6.x + 6 . 1
x³ + x² - 5x² - 5x + 6x + 6
=> x³ - 4x² + x + 6

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Resolvendo pelos dois primeiros termos:

(x + 1) . (x - 2) . (x - 3)

(x . x - x.2 + 1.x - 1. 2) . (x - 3)
(x² - 2x + x - 2) . (x - 3)
(x² - x - 2).(x - 3)
x² . x - x².3 - x.x + x.3 - 2.x + 2.3
x³ - 3x² - x² + 3x - 2x + 6
=> x² - 4x² + x + 6