Question 112196
Since the numerator is a difference of cubes, we can use the difference of cubes formula


Remember, the difference of cubes formula is {{{a^3-b^3=(a-b)(a^2+ab+b^2)}}}


So {{{x^3-a^3}}} becomes {{{(x-a)(x^2+ax+a^2)}}}



So {{{(x^3-a^3)/(x-a)}}} then becomes {{{(x-a)(x^2+ax+a^2)/(x-a)}}}



Now cancel like terms



{{{cross((x-a))(x^2+ax+a^2)/cross((x-a))}}}



Simplify



{{{x^2+ax+a^2}}}




So  {{{(x^3-a^3)/(x-a)}}}  simplifies to {{{x^2+ax+a^2}}}