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In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First ("first" terms of each binomial are multiplied together)
An example of multiplying binomials is (2x+1)×(x+2) and the first step the student would take is set up two positive x tiles and one positive unit tile to represent the length of a rectangle and then one would take one positive x tile and two positive unit tiles to represent the width. These two lines of tiles would create a space that looks ...
Above, the resulting (+) in the second line is evaluated by the second application of the binomial expansion, introducing another summation over the index . The product of the two binomial coefficients is simplified by shortening r ! {\displaystyle r!} ,
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product = is a product distribution.
Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic or powering of matrices. For semigroups for which additive notation is commonly used, like elliptic curves used in cryptography , this method is also referred to as double-and-add .
The second study design is given by the product of two independent binomial distributions; the totals in one of the margins (either the row totals or the column totals) are constrained by the experimental design, but the totals in other margin are free. This is by far the most common form of experimental design, where the experimenter ...
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