Chứng minh rằng: (x - y)(xn - yn) chia hết cho (x - y)^2
Giải thích
Ta có xn – yn = (x – y)(xn–1 + xn–2y + xn–3y2 +…+ xyn–2 + yn–1)
Vì x – y chia hết cho x – y nên (x – y)(xn–1 + xn–2y + xn–3y2 +…+ xyn–2 + yn–1) chia hết cho x – y.
Suy ra (x – y)(x – y)(xn–1 + xn–2y + xn–3y2 +…+ xyn–2 + yn–1) chia hết cho (x – y)2
Vậy (x – y)(xn – yn) chia hết cho (x – y)2.