please help with factoring algebraic expressions

Question

I was given the problem $144x^4-121x^2y^2+16y^4.$ I used completing the square and got an answer of $12x^2+4y^2+11ixy$, I would like to know if this is correct.

Answer 1

try the Ansatz $$(12x^2-...-4y^2)(12x^2+...-4y^2)$$

Answer 2

Hint

It is not correct.

Try this one:

Complete square for the terms $144x^4$ and $16y^4$ and get $$144x^4+ 16y^4=(12x^2-4y^2)^2+96x^2y^2$$

now use the whole thing

$$144x^4-121x^2y^2+16y^4=(12x^2-4y^2)^2+96x^2y^2-121x^2y^2=(12x^2-4y^2)^2-(5xy)^2$$

Can you finish?