Question

How to prove (x^n - a^n)/(x-a ) = (x-a)(x^ (n-1) + x^(n-2) a +….a^ (n-1))? Please help.Thanks

Answer 1

you can prove it by using synthetic division and divide x^n - a^n by x-a

First step
x^n - a^n - x^n-1 (x-a) = x^n-1 a - a^n

Second step
x^n-1 a - a^n - x^n-2 a (x-a ) = x^n-2 a^2 - a^n
. . .until the exponent of x become 0

Hope this helps