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You are right. It is a bit obscure, but it is something that comes in handy from time to time. Every once in a while you will get some questions but this one is good to know and should be added to the list. (such as The formula for difference of cubes is good to know. Sometimes we are finding the difference of literal 3D objects and  Difference of cubes is SOAP. Same Opposite Always Positive. For example (A^3 - B^3) = (A-B)(A^2+AB+B^2)

You will see questions, or derivations like them on the test. Really, it is a f(c) = y where f(x)/(x-c) has a remainder equal to y.

So its not necessarily the difference of cubes that is being tested but their understanding of the remainder theorem and polynomials in general.

The student could have substituted D^(2/3) for A and F^(2/3) for B then found the difference of squares, in a sense.

Because the question had answer choices, it must have been an "equivalent" question. In this case, the purpose could also be to test deductive reasoning by plugging in values .