Question

I need a explanation for this

Answer 1

\[\frac{ a^n-b^n }{ a-b } = a^\left( n-1 \right)+a^\left( n-2 \right)*b......+a*b^\left( n-2 \right)+b^\left( n-1 \right)\]

Answer 2

its just division ...

Answer 3

a^(n-1)
-----------
a-b | a^n - b^n
(a^n -a^(n-1)b)
---------------
a^(n-1)b - b^n






a^(n-1) +a^(n-2)b
-----------
a-b | a^n - b^n
(a^n -a^(n-1)b)
---------------
a^(n-1)b - b^n
(a^(n-1)b -a^(n-2)b^2)
---------------------
a^(n-2)b^2 - b^n