翻訳と辞書 Words near each other ・ Polyortha chiriquitana ・ Polyortha chlamydata ・ Polyortha clarkeana ・ Polyortha euchlorana ・ Polyortha evestigana ・ Polyortha glaucotes ・ Polynomial and rational function modeling ・ Polynomial arithmetic ・ Polynomial basis ・ Polynomial chaos ・ Polynomial code ・ Polynomial conjoint measurement ・ Polynomial decomposition ・ Polynomial delay ・ Polynomial Diophantine equation ・ Polynomial expansion ・ Polynomial function theorems for zeros ・ Polynomial greatest common divisor ・ Polynomial hierarchy ・ Polynomial identity ring ・ Polynomial interpolation ・ Polynomial kernel ・ Polynomial least squares ・ Polynomial lemniscate ・ Polynomial long division ・ Polynomial matrix ・ Polynomial regression ・ Polynomial remainder theorem ・ Polynomial representations of cyclic redundancy checks ・ Polynomial ring Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Polynomial expansion ： ウィキペディア英語版 Polynomial expansion In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a sum of (repeated) products. During the expansion, simplifications such as grouping of like terms or cancellations of terms may also be applied. Instead of multiplications, the expansion steps could also involve replacing powers of a sum of terms by the equivalent expression obtained from the binomial formula; this is a shortened form of what would happen if the power were treated as a repeated multiplication, and expanded repeatedly. It is customary to reintroduce powers in the final result when terms involve products of identical symbols. Simple examples of polynomial expansions are the well known rules :$(x+y)^2=x^2+2xy+y^2$ :$(x+y)(x-y)=x^2-y^2$ when used from left to right. A more general single-step expansion will introduce all products of a term of one of the sums being multiplied with a term of the other: :$(a+b+c+d)(x+y+z)=ax+ay+az+bx+by+bz+cx+cy+cz+dx+dy+dz$ An expansion which involves multiple nested rewrite steps is that of working out a Horner scheme to the (expanded) polynomial it defines, for instance :$1+x(-3+x(4+x(0+x(-12+x\backslash cdot\; 2))))=1-3x+4x^2-12x^4+2x^5$. The opposite process of trying to write an expanded polynomial as a product is called polynomial factorization. ==Expansion of a polynomial written in factored form== To multiply two factors, each term of the first factor must be multiplied by each term of the other factor. If both factors are binomials, the FOIL rule can be used, which stands for "First Outer Inner Last," referring to the terms that are multiplied together. For example, expanding : $(x+2)(2x-5)\backslash ,$ yields : $2x^2-5x+4x-10\; =\; 2x^2-x-10.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Polynomial expansion」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.