Algebra
posted by Laura on .
How can you determine if a polynomial is the difference of two squares? I think that if the polynomial is x^264 that this is a polynomial that is a difference of two squares because if you factor it out you would get
(x+8)(x8).
If the 64 in my example were positive would there still be a difference between two squares since x^2 and 64 both are squared numbers?

No, when it says difference, it needs the single  sign.
(ab)(a+b) = a^2 + ab ab  b^2 = a^2b^2
but
(a+b)(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2 which is no good 
Oh and x^2+64
solve x^2 + 0x + 64 = 0
x = [0 +/ sqrt (0 256) / 2
x = +/ sqrt (256) /2
x = +/ 8 i
so
x*2+64 = (x8i)(x+8i)
In other words there is no real number solution, You need the sqrt of 1 or "i"