Express x3+y3+z3−3xyz as a product of two polynomials.
(i) Write the general factorised form of a3+b3+c3−3abc.
(ii) Using the result from part (i), factorise x3+y3+z3−3xyz completely.
(iii) Explain why the factor (x+y+z) must always appear in the factorisation obtained in part (ii).