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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 ...
A golden rectangle with long side a + b and short side a can be divided into two pieces: a similar golden rectangle (shaded red, right) with long side a and short side b and a square (shaded blue, left) with sides of length a. This illustrates the relationship a + b / a = a / b = φ.
Applying Legendre's formula to the product formula for binomial coefficients produces Kummer's theorem, a similar result on the exponent of each prime in the factorization of a binomial coefficient. [55] Grouping the prime factors of the factorial into prime powers in different ways produces the multiplicative partitions of factorials. [56]
In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform. dim – dimension of a vector space.
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [1] [2] [3] On an expression or formula calculator, one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
The formula calculator concept can be applied to all types of calculator, including arithmetic, scientific, statistics, financial and conversion calculators. The calculation can be typed or pasted into an edit box of: A software package that runs on a computer, for example as a dialog box. An on-line formula calculator hosted on a web site.
This equation states that , representing the square of the length of the side that is the hypotenuse, the side opposite the right angle, is equal to the sum (addition) of the squares of the other two sides whose lengths are represented by a and b. An equation is the claim that two expressions have the same value and are equal.