Question

factorize
x²-an-bn+ab​

Answer 1

Wikipedia provides a proof, but I don't understand how:

an−bn=(a−b)(an−1+ban−2+⋯+bn−1)

follows from

xn−1+xn−2+⋯+x+1=xn−1x−1

Could someone explain to me how the summation of the the geometric series explains the factorization?