Freshman's dream

Common card · No. 402386

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 = x n + y n {\displaystyle (x+y)^{n}=x^{n}+y^{n}} . Beginning students commonly make this error in computing the power of a sum of real numbers, falsely assuming powers distribute over sums. If the theorem held in a general case it would often make algebraic manipulations far easier; hence, it is humorously referred to as the freshman's "dream". The correct result is given by the binomial theorem, which has additional terms in the middle when n ≥ 2 {\displaystyle...

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