How does this expression demonstrate mathematical telescoping? What exactly *is* telescoping? Here is the expression:
$x^n-y^n$
According to my professor, this is factorable, and an example for telescoping in mathematics. I've gleaned some sense of what Telescoping is from this answer: Mathematical Telescoping. Could someone walk me through how the above expression can be factored, and how it exhibits telescoping (and why telescoping is salient to begin with?).

In my view this is the result of a telescoping sum. From the formula of the partial sum of a geometric series it can be derived that
$(x-y)\cdot \sum_{k=0}^{n-1} x^k\cdot y^{n-k-1}=x^n-y^n$
$\sum_{k=0}^{n-1} \left( x^{k+1}\cdot y^{n-k-1}-x^k\cdot y^{n-k}\right)$
$=x\cdot y^{n-1}-y^{n}+x^2\cdot y^{n-2}-x\cdot y^{n-1}+x^3\cdot y^{n-3} -x^2\cdot y^{n-2}+\ldots+x^{n-1}\cdot y -x^{n-2}\cdot y^2 +x^n-x^{n-1}\cdot y $
I think you see that only $x^n-y^n$ remains. You can see that the most positive summands have a corresponding negative summand as well. The consequence is that a series can be simplified by using the fact that the sum of these pairs of summands are $0$. 
