a^3 – 3a^2b + 3ab^2 – b^3
(a – b )(a – b)
If I did not recognize that the numerator was the difference of cubes and that I could factor out (a-b)^2 from numerator and denominator, could this be solved using polynomial division?
It could! But if you recognize a shortcut, why do the long way? 🙂
(Just to make sure nobody gets confused, the numerator here isn’t a difference of cubes; it’s actually a regular old binomial cube. That numerator factors to . So what you really have in this question is which of course simplifies to plain old .)