Also useful is Lagrange's Identity:
(a^2+b^2)(c^2+d^2) = (ac-bd)^2+(ad+bc)^2
Express (x^2+a^2)(y^2+b^2)(z^2+c^2) as a sum of two squares
One way to go is via complex numbers.
Hint: Take z1 = x + ia, z2 = y + ib, z3 = z+ic
And use the fact that
|z1 z2 z3| = |z1| |z2| |z3|
yup exactly...
And this is what i wanted the users to think like.. but alas ;)
Also useful is Lagrange's Identity:
(a^2+b^2)(c^2+d^2) = (ac-bd)^2+(ad+bc)^2