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The freshman's dream is a name sometimes given to the erroneous equation {\displaystyle (x+y)^{n}=x^{n}+y^{n}}, where {\displaystyle n} is a real number (usually a positive integer greater than 1) and {\displaystyle x,y} are nonzero real numbers. Beginning students commonly make this error in computing the power of a sum of real numbers, falsely assuming powers distribute over sums.[1][2] 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 as the FOIL method). For larger positive integer values of n, the correct result is given by the binomial theorem.
Freshman's Dream - Wikipedia
FOIL method
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Why sex? Surely there are features of human nature other than this one overexposed and troublesome procreative pastime: True enough, but reproduction is the sole goal for which human beings are designed;
The Red Queen: Sex and the Evolution of Human Nature
Matt Ridley
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