Hi,
How do I start this?
Express $\displaystyle x^4 + y^4 + z^4 - 2y^2z^2 - 2z^2x^2 - 2x^2y^2$ as the product of four factors.
If you put the numbers (x,y,z) = (2,1,1) your expression is zero. This means (x-y-z) could be a factor. By symmetry, (-x+y-z) and (-x-y+z) could also be factors. Last, (-2,1,1) also makes your expression zero. So (x+y+z) should be a factor. Try multiplying:
$\displaystyle
(x-y-z)(-x+y-z)(-x-y+z)(x+y+z)
$