Is it possible to simplify this expression? I'm hoping that the expression can be written into some quadratic form but I have no idea if that is possible.
Rewrite your function as
Let be a function of x and y which is a multinomial (does not have square roots in it). (Note that might equal zero or some other constant)
If that function does factorise then it can be written as
From this you can determine that
and
From:
You can determine that
and
h(x,y) is simple enough that you can tell it cannot be factored any more (Well actually can be factorised but it involves imaginary numbers so ignore that)
Since
You can rewrite that as
You know g(x,y) and so you can do the long division. When you do the long division you will get a remainder. The remainder is equal to
That's as much progress as I can make towards getting the factors. Maybe you can work out the next step. This is very involved for pre-university maths.
First of all, thanks for your very helpful feedback. It gives me quite some things work with.
I missed a square in the expression, it should read
Shouldn't your equation
read
instead?
I was hoping that I could do the following factorization
but that seems like not possible.