The other tutor gave a partial factorization but not 
the complete factorization.  Let's go for the complete 
factorization, not just show that we can factor out 3.



This is a third degree polynomial in three variables.

Set it equal to 0, and look for its zeros:



If we assume x=-y we get







So since x=-y  gives an identity, that means that

(x+y) is a factor of the given polynomial.

In exactly the same way, by symmetry x=-z and y=-z will 
also give an identity.

Therefore (x+y)(x+z)(y+z) must be a factor of the original
polynomial.

Since this will yield a third degree polynomial when
multiplied out, it can only be different from the factorization
of the original polynomial by a non-zero constant factor.

So the factorization must be:

, 

for some non-zero constant k. So



must be an identity for all values of x,y, and z

Let's choose x = 1, y = 1, z = 0











Therefore the factorization 

becomes



That took longer than 30 seconds!  Sorry! But we got it done :)

Edwin