Freshman's Dream - Wikipedia - FOIL method  ## Metadata - Author: **FOIL method** - Full Title: Freshman's Dream - Wikipedia - Category: #articles - URL: https://en.wikipedia.org/wiki/Freshman%27s_dream ## Highlights - 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. - Tags: #mathematic