Question

Factorize x^4+y^4+(x+y)^4

Answer 1

if you fully expand this out it becomes:
2x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + 2y^4

Answer 2

i'm thinking the simplest factorization is either:
2(x^2 + x y + y^2)^2

or

x^4 + y^4 + (x+y)(x+y)(x+y)(x+y)