SOLUTION: how do you determine if a polynomial is the difference of two squares?
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Question 400282: how do you determine if a polynomial is the difference of two squares?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A polynomial is the difference of two squares if it has exactly two positive terms and there is a minus sign between them. Typically the situations that arise in beginning and intermediate algebra have two terms that are each perfect squares so that the conjugate pair factorization is nice and tidy, thus:
However any positive number is the square of something, even if it isn't rational.
Hence,
where
and 
is the difference of two squares if you write it thus:
^2\ -\ \left(\sqrt{y}\right)^2)
And the factorization would be:
\left(\sqrt{x^3}\ -\ \sqrt{y}\right))
John
My calculator said it, I believe it, that settles it
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