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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]
The term "freshman's dream" itself, in non-mathematical contexts, is recorded since the 19th century. [ 9 ] Since the expansion of ( x + y ) n is correctly given by the binomial theorem , the freshman's dream is also known as the " child's binomial theorem " [ 4 ] or " schoolboy binomial theorem ".
In either case, the use or non-use of the term "FOIL" is moot. - dcljr 22:24, 3 September 2009 (UTC) How new is the FOIL method? The oldest (only) reference in the article is 1997. If it's a new pedagogical device then it's not too surprising to see it meeting some resistance, especially by those opposed to learning by memorizing rules.
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 ...
Layers of Pascal's pyramid derived from coefficients in an upside-down ternary plot of the terms in the expansions of the powers of a trinomial – the number of terms is clearly a triangular number. In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by
Just [cook] straight at 325°F, which for a 15- to 16-pound bird, should take three to three-and-a-half-hours to roast.” “To check for doneness, we always recommend a meat thermometer ...
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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.