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.

• That is correct Commented Sep 11, 2017 at 12:35
• Have you tried checking your own work first by multiplying out your answer (which, presumably, is actually $(12x^2+4y^2+11ixy)^2$) to see if you get the original expression?
– amd
Commented Sep 12, 2017 at 1:27
• It looks to me like you simply took to square roots of all of the coefficients.
– amd
Commented Sep 13, 2017 at 1:54

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

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?

• where did the *5xy)^2 come from? Commented Sep 11, 2017 at 12:40
• @user370026: take another look. It is clear? Commented Sep 11, 2017 at 12:43
• i would like to know why you added 96x^2y^2 Commented Sep 11, 2017 at 12:47
• @user370026: I am completing square. Commented Sep 11, 2017 at 12:49
• @user370026: Is it clear? Commented Sep 12, 2017 at 12:14