I am working with a Frenchman and need to talk about the difference of two squares. Would that be 'La différence des deux carrés'?

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    off-topic, but "yes". – Carlo Beenakker Nov 25 '16 at 16:04

If the two squares you consider are well defined, it's indeed "la différence des deux carrés", where "des" stands for "de les". Otherwise, if you consider two squares without any precise knowledge of what they're expected to be, it will be "la différence de deux carrés". 31 est la différence de deux carrés. La différence des deux carrés 256 et 225 est 31.

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Différence de[s] deux carrés and différence des carrés are indeed the phrases commonly used when talking about the generic, mathematical formula.

Entre might also be used instead of de/des, especially when talking about actual numbers:

La différence de 16 et 25

La différence entre 16 et 25

The latter might also refer to something else than the numerical difference, like for example 16 est pair mais 25 est impair.

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  • To me, "la différence de 25 et de 16" is the very result of the substraction 25-16. "La différence entre 16 et 25" is either the distance between those numbers or some property that distinguishes them. – Sylvain JULIEN Nov 27 '16 at 10:16
  • @SylvainJULIEN Hmm, yes, you are right. To my surprise I see many occurrences of la différence de x et de y. For some reason, I find de odd when used with différence but fine with the other basic operations: la somme de a et de b, le produit de a et de b, le quotient de a et b. Answer updated. Thanks. – jlliagre Nov 27 '16 at 10:36

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