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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]
[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).
In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently, the polynomial method has led to the development of remarkably simple solutions to several long-standing open problems ...
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 method of equating coefficients is often used when dealing with complex numbers. For example, to divide the complex number a + bi by the complex number c + di , we postulate that the ratio equals the complex number e+fi , and we wish to find the values of the parameters e and f for which this is true.
Given a quadratic polynomial of the form + + it is possible to factor out the coefficient a, and then complete the square for the resulting monic polynomial. Example: + + = [+ +] = [(+) +] = (+) + = (+) + This process of factoring out the coefficient a can further be simplified by only factorising it out of the first 2 terms. The integer at the ...
Polynomial factorization is one of the fundamental components of computer algebra systems. The first polynomial factorization algorithm was published by Theodor von Schubert in 1793. [1] Leopold Kronecker rediscovered Schubert's algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension.
Since 9 = 10 − 1, to multiply a number by nine, multiply it by 10 and then subtract the original number from the result. For example, 9 × 27 = 270 − 27 = 243. 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.