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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]
Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.
The product operator for the product of a sequence is denoted by the capital Greek letter pi Π (in analogy to the use of the capital Sigma Σ as summation symbol). [1] For example, the expression ∏ i = 1 6 i 2 {\displaystyle \textstyle \prod _{i=1}^{6}i^{2}} is another way of writing 1 ⋅ 4 ⋅ 9 ⋅ 16 ⋅ 25 ⋅ 36 {\displaystyle 1 ...
1.4 Limits involving derivatives or infinitesimal changes. 1.5 Inequalities. 2 Polynomials and functions of the form x a. ... This is the product rule.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). Thus 16 × 5 = 80 is twice the sum.
In mathematics, for a sequence of complex numbers a 1, a 2, a 3, ... the infinite product ∏ n = 1 ∞ a n = a 1 a 2 a 3 ⋯ {\displaystyle \prod _{n=1}^{\infty }a_{n}=a_{1}a_{2}a_{3}\cdots } is defined to be the limit of the partial products a 1 a 2 ... a n as n increases without bound.
An algebraic operation may also be defined more generally as a function from a Cartesian power of a given set to the same set. [4] The term algebraic operation may also be used for operations that may be defined by compounding basic algebraic operations, such as the dot product.
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