Chứng minh: a) (x + 1)(x^2 – x + 1) = x^3 – 1.
Giải thích
a) (x + 1)(x2 – x + 1)
= x . (x2 – x + 1) + 1 . (x2 – x + 1)
= x . x2 – x . x + x . 1 + x2 – x + 1
= x3 – x2 + x + x2 – x + 1
= x3 + (– x2 + x2) + (x – x) + 1
= x3 – 1.
Vậy (x + 1)(x2 – x + 1) = x3 – 1.