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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 "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 ]
[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.
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 ...
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).
Can you vary or change your problem to create a new problem (or set of problems) whose solution(s) will help you solve your original problem? Search: Auxiliary Problem: Can you find a subproblem or side problem whose solution will help you solve your problem? Subgoal: Here is a problem related to yours and solved before
California GOP leaders are calling for more accountability after the state auditor found that despite roughly $24 billion spent on homeless and housing programs during the 2018-2023 fiscal years ...
Contemporary Marxists regard Marxist theory as a source of actual knowledge, but Sartre sees it only as a set of problems in search of a method. [24] As in the first chapter, Sartre sees Marxism's flaw in rigidity: an "a priori" theory that forces events into "prefabricated molds." [25] Sartre again turns to