Factor the expression completely over the complex numbers.

y^4+12y^2+36

Y⁴ + 12y² + 36

Now factorize the expression

y⁴ + 6y² + 6y² + 36

= y² (y² + 6) + 6 (y² + 6)

= (y² + 6) (y² + 6)

Now 6 is not the perfect square and according to rule, binomial can not be factored as the difference of two perfect squares.

so multiply both.

(y² + 6) ² is the answer.