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The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
Don Quixote and his sidekick Sancho Panza, as illustrated by Gustave Doré: the characters' contrasting qualities [1] are reflected here even in their physical appearances. In any narrative, a foil is a character who contrasts with another character, typically, a character who contrasts with the protagonist, in order to better highlight or differentiate certain qualities of the protagonist.
Like the ID3 algorithm, FOIL hill climbs using a metric based on information theory to construct a rule that covers the data. Unlike ID3, however, FOIL uses a separate-and-conquer method rather than divide-and-conquer, focusing on creating one rule at a time and collecting uncovered examples for the next iteration of the algorithm. [citation ...
[1] [2] When n = 2, it is easy to see why this is incorrect: (x + y) 2 can be correctly computed as x 2 + 2xy + y 2 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.
The term "FOIL rule" is rarely used, "FOIL method" is an order of magnitude more common. I suggest moving the article accordingly. -- Vaughan Pratt ( talk ) 19:04, 6 September 2009 (UTC) [ reply ]
The last image we have of Patrick Cagey is of his first moments as a free man. He has just walked out of a 30-day drug treatment center in Georgetown, Kentucky, dressed in gym clothes and carrying a Nike duffel bag.
This method can be adjusted to multiply by eight instead of nine, by doubling the number being subtracted; 8 × 27 = 270 − (2×27) = 270 − 54 = 216. Similarly, by adding instead of subtracting, the same methods can be used to multiply by 11 and 12, respectively (although simpler methods to multiply by 11 exist).
Using this method, Gu and his colleagues determined that every 18 seconds, sections of the crowd about 500 people strong unwittingly found themselves traveling in the same direction and making a ...