factorization of a fourth degree polynomial

Question

What could be the possible factorization of $$2a^4+a^2b^2+ab^3+b^4$$? what term should be added

Answer 1

Hint : $(a^2+b^2)^2-a^2b^2=a^4+a^2b^2+b^4$

$$(a^2-a b+b^2) (2 a^2+2 a b+b^2)$$

Answer 2

HINT:

$$a^4+a^2b^2+b^4+a(a^3+b^3)$$

$$=(a^2-ab+b^2)(a^2+ab+b^2)+a(a+b)(a^2-ab+b^2)$$