Question

How do you determine if a polynomial is the difference of two squares?

Answer 1

For Example

Answer 2

A binomial with an exponential variable and negative number followed

If you can take the square root of both the variable and the number after it

The reason for both answers is, because whenever you take the square root of any number, you will get a positive and negative answer of the same number.


For example:

x^2-25 = (x+5)(x-5)

If it were x^2+25,

There wouldn't be a real answer, but will still be factorable in the imaginary scale
(x+5i)(x-5i)
--

even if it was

x^4-25,
it would equal
(x^2+5)(x^2-5), because you took the squareroot of the t^4 and the 25.

Answer 3

Simple for quadratics, remember
\[Y=a(x-k)^{2}+h\]

if h is a negative number then your polynomial of degree two is a difference of two squares and what look as follows

\[Y=(\sqrt{a}(x-k))^{2}-(\sqrt{h})^{2}\]

factor the negative and square root the h, then square square root.

For polynomials of higher degrees reduce them in pairs and if at the end you a bunch of squares added and subtracted together then it's a difference of squares....Note: Easier said than done.

Answer 4

same thing if a is negative.....can't be done if both "a" and "h" are negative.