Question

Mathematical Induction Question:

Prove using MI : ( x^n - y^n) is divisible by (x-y)

Answer 1

\[x^{n+1}-y^{n+1}=x^{n+1}-xy^n+xy^n-y^{n+1}+x^ny-x^ny=\]
\[=x(x^n-y^n)+y(x^n-y^n)-xy(x^{n-1}-y^{n-1})=\]
\[=(x+y)(x^n-y^n)-xy(x^{n-1}-y^{n-1})\]
this is divisible by x-y

Answer 2

How is this divisible by x-y ?