(x - 1)³ - 2x (x - 1)² + (x - 1) (x + 1) (x - 2) = (x - 1) ( (x - 1)² - 2x (x - 1) + (x + 1)(x - 2) )
= (x - 1) ( (x - 1) (x - 1 - 2x) + (x + 1)(x - 2) )
= (x - 1) ( (x - 1) (- x - 1) - (-x - 1)(x - 2) )
= (x - 1) ( (-x - 1) (x - 1 - x + 2) )
= (x - 1) ( (-x - 1) (1) )
= (x - 1) (- x - 1)
= - (x - 1) (x + 1)
= 1 - x²
