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Freshman's dream

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In mathematics, the freshman's dream, also known as freshman exponentiation, the child's binomial theorem, (rarely) the schoolboy binomial theorem, or the Frobenius identity is the generally-false equation (x + y)n = xn + yn. Beginning students commonly make this error in computing the power of a sum of real numbers, falsely assuming powers distribute over sums.

Freshman's dream - Wikipedia Jump to content From Wikipedia, the free encyclopedia Mathematical fallacy An illustration of the Freshman's dream in two dimensions. Each side of the square is X+Y in length. The area of the square is the sum of the area of the yellow region (=X 2 ), the area of the green region (=Y 2 ), and the area of the two white regions (=2×X×Y). In mathematics, the freshman's dream , [ 1 ] [ 2 ] [ 3 ] [ 4 ] also known as freshman exponentiation , [ 4 ] [ 5 ] the child 's binomial theorem , [ 6 ] (rarely) the schoolboy binomial theorem , [ 7 ] or the Frobenius identity [ 3 ]

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