(X-1)(X^2 + X + 1)
= XX^2 + XX + X - X^2 - X - 1
= X^3 + X^2 + X - X^2 - X - 1
= X^3 + 0X^2 + 0X - 1
= X^3 - 1
(X-1)(X^2 + X + 1)
= XX^2 + XX + X - X^2 - X - 1
= X^3 + X^2 + X - X^2 - X - 1
= X^3 + 0X^2 + 0X - 1
= X^3 - 1