Can the sum of squares ever be factored?

Question

One of my algebra questions is "Can the sum of squares ever be factored?" I am thinking no but I'm not sure.

Answer 1

No, to find zeros of sum of square you'd need to use quadratic formula.

Answer 2

No.

I think you'd get imaginary numbers.Only the difference of squares.

Answer 3

No, except if you have something like 8^2 +1 which is ALSO the sum of two cubes: 8^2 +1^2 = 4^3 + 1^3 = (4+1)(4^2 -4 +1) =5 x 13