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

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Answer 1 · 2016-03-20T01:39:30

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

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

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:

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

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