Freshman's dream

Mathematical fallacy

The freshman's dream is a name given to the erroneous equation , where is a real number (usually a positive integer greater than 1) and are non-zero real numbers. Beginning students commonly make this error in computing the power of a sum of real numbers, falsely assuming powers distribute over sums. When n = 2, it is easy to see why this is incorrect: (x + y)2 can be correctly computed as x2 + 2xy + y2 using distributivity (commonly known by students in the United States as the FOIL method). For larger positive integer values of n, the correct result is given by the binomial theorem.

This keyword could refer to multiple things. Here are some suggestions: