Vijay

The way one should approach math problems is by looking at the question and given statements as one detail. Then we direct our thinking to see a relation between the question asked and provided comments. Now coming to the problem itself, it's a polynomial question with submitted statements of degree 2 and question statement is of degree 3. How do I transition from given reports to arrive the given problem, which is also a way of asking oneself what should I multiply the 2nd-degree polynomial to make it 3rd degree? Voila (x + y+ z) looking at the question as a whole.

(x + y+ z)( x² +y² +z²) = (x + y+ z)(xy + yz + zx)

x³ + xy² + xz²  + yx² + y³ + yz² + zx² + zy² + z³  =  x²y + xyz + zx² + xy² + y²z + xyz + xyz + yz² + z²x

..rearranging and cancelling equaling terms final leads to ..

x³ + y³ + z³  =  xyz  + xyz + xyz

x³ + y³ +z³ = 3xyz

so the answer is 3xyz.

Note: it's not the answer which is essential but the way you approach the problem leading it to the answer is really what matters! In short, it's the mathematical thinking which is required then the answer itself!