Question

How can you determine if a polynomial is the difference of two squares? I think that if the polynomial is x^2-64 that this is a polynomial that is a difference of two squares because if you factor it out you would get
(x+8)(x-8).
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?

Answer 1

No, when it says difference, it needs the single - sign.
(a-b)(a+b) = a^2 + ab -ab - b^2 = a^2-b^2
but
(a+b)(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2 which is no good

Answer 2

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 = (x-8i)(x+8i)
In other words there is no real number solution, You need the sqrt of -1 or "i"