SAT - difference of cubes? – Khan Academy Help Center

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10 september 2020 20:17

I was working with a student a couple of weeks ago when we encountered a practice problem that required her to factor a difference of cubes.

I was surprised to see that concept among the practice problems, and a Google search didn't include it among any of the SAT "formulas you must know" or "concepts you must know". Since it isn't as common as the rest of the Algebra II concepts I have seen on the SAT practice, I have to wonder - is it actually likely to be included on the new SAT? I don't see it as something you would derive in under 5 minutes, so the even the above-average student would either have it memorized (and be able to use it) or they wouldn't, and normally the SAT doesn't require that level of simple memorization to solve problems

Does anyone know if it is something that you need to have memorized, or was that a fluke of the Khan Academy practice problems?

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michael

12 september 2020 12:52
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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 .

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SAT - difference of cubes?

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