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

Question

anonymous · Answer

To some extent it is by practice recognizing the difference of two squares.  If I see the first term is squared and there are only two terms such as
a^2 - something
then I will immediately check to see if the second term is a perfect square, if so then it would be a difference such as
(a-b)(a+b)

anonymous · Answer

The general form of a 'difference of two squares' will be $$a^2x^2-b^2$$ Which makes sense if you consider that the factors of this will be $$(ax+b)(ax-b)$$ You can multiply out those brackets, and get back to the initial expression.

anonymous · Answer

by observation - 0ne perfect square  - another
eg
x^2 - 4
4y^2 - 9v^2

anonymous · Answer

The key is that there is no term $cx$; and the $ax^2$ and the $b^2$ are separated by a minus sign.