ILL GIVE A MEDAL JUST HELP

I'm supposed to factor this four-term polynomial by grouping:

x^4 - 2x^2 + 2y^2 + 10

What I've done so far:

I have split the polynomial into 2 sections:

(x^4 – 2x^2) + (2y^2 + 10)

I have brought GCF's from both binomials to outside the parentheses:

x^2(x^2 - 2) + 2(y^2 + 5)

But now I'm stuck. How do I factor x^4 - 2x^2 + 2y^2 + 10 from here? Please help, but I'm under a bit of time pressure because I have to sleep, so please don't take too long. Thanks!

Question

ILL GIVE A MEDAL JUST HELP

I'm supposed to factor this four-term polynomial by grouping:

x^4 - 2x^2 + 2y^2 + 10

What I've done so far:

I have split the polynomial into 2 sections:

(x^4 – 2x^2) + (2y^2 + 10)

I have brought GCF's from both binomials to outside the parentheses:

x^2(x^2 - 2) + 2(y^2 + 5)

But now I'm stuck. How do I factor x^4 - 2x^2 + 2y^2 + 10 from here? Please help, but I'm under a bit of time pressure because I have to sleep, so please don't take too long. Thanks!

anonymous · Answer

@zepdrix @triciaal @mathstudent55 @satellite73 @mathmale

anonymous · Answer

@Owlcoffee @ anyone else who can help with this

owlcoffee · Answer

Yes, I think we can bring this to the structure:
$$(a+b)^2=a^2+2ab+b^2$$
But that'll make things a lot more complicated. 
I don't seem to be able to find any better answer than:
$$x^2(x^2-2)+2(y^2+5)$$
Since it's the most simple form and not further reducible.

crabbyoldgamer · Answer

You're at a point where it is not possible to factor further.

anonymous · Answer

So x^2(x^2 - 2) + 2(y^2 + 5) would be fully simplified?

crabbyoldgamer · Answer

Yes

crabbyoldgamer · Answer

Unless you entered the problem incorrectly.

anonymous · Answer

@crabbyoldgamer Alright, thanks for helping!