Question

How do you long divide `(x^5 - x^5) /( x - y)`?

Answer 1

Assuming the second `x^5` should have been a `y^5`:

`(x^5-y^5)/(x-y) = x^4+x^3y+x^2y^2+xy^3+y^4`

Explanation:

See my answer:

http://socratic.org/questions/how-do-you-divide-x-6-y-6-x-y

where I long divide the coefficients for `(x^6-y^6)/(x-y)` and discuss the general case of `(x^n-y^n)/(x-y)`

The present example works out similarly:

`(x^5-y^5)/(x-y) = x^4+x^3y+x^2y^2+xy^3+y^4`