Multiply :

x² + x + 1 by 1 - x

(x² + x + 1) $\times$ (1 - x)

= 1 $\times$ (x² + x + 1) - x $\times$ (x² + x + 1)

= (1 $\times$ x² + 1 $\times$ x + 1 $\times$ 1) - (x $\times$ x² + x $\times$ x + x $\times$ 1)

= x² + x + 1 - (x³ + x² + x)

= x² + x + 1 - x³ - x² - x

= (x² - x²) + (x - x) + 1 - x³

= 1 - x³

Hence, (x² + x + 1) $\times$ (1 - x) = 1 - x³