Editing Elementary algebra (section)

==Algebraic notation ==
{{main|Mathematical notation}}
Algebraic notation describes the rules and conventions for writing [[Expression (mathematics)|mathematical expressions]], as well as the terminology used for talking about parts of expressions. For example, the expression <math style="margin-bottom:8px">3x^2 - 2xy + c</math> has the following components:

[[File:algebraic equation notation.svg|256px|thumb|center|Algebraic expression notation:<br />&nbsp; 1 – power (exponent)<br />&nbsp; 2 – coefficient<br />&nbsp; 3 – term<br />&nbsp; 4 – operator<br />&nbsp; 5 – constant term<br />&nbsp; <math>c</math> – constant<br />&nbsp; <math>x</math> <math>y</math> – variables]]

A ''coefficient'' is a numerical value, or letter representing a numerical constant, that multiplies a variable (the operator is omitted). A ''term'' is an [[Addend#Notation and terminology|addend or a summand]], a group of coefficients, variables, constants and exponents that may be separated from the other terms by the plus and minus operators.<ref>Richard N. Aufmann, Joanne Lockwood, ''Introductory Algebra: An Applied Approach'', Publisher Cengage Learning, 2010, {{ISBN|1439046042}}, 9781439046043, [https://books.google.com/books?id=MPIWikTHVXQC&q=coefficient+&pg=PA78 page 78]</ref> Letters represent variables and constants. By convention, letters at the beginning of the alphabet (e.g. <math>a, b, c</math>) are typically used to represent [[Mathematical constant|constant]]s, and those toward the end of the alphabet (e.g. <math>x, y</math> and {{mvar|z}}) are used to represent [[Variable (mathematics)|variable]]s.<ref>William L. Hosch (editor), ''The Britannica Guide to Algebra and Trigonometry'', Britannica Educational Publishing, The Rosen Publishing Group, 2010, {{ISBN|1615302190}}, 9781615302192, [https://books.google.com/books?id=ad0P0elU1_0C&q=letters&pg=PA71 page 71]</ref> They are usually printed in italics.<ref>James E. Gentle, ''Numerical Linear Algebra for Applications in Statistics'', Publisher: Springer, 1998, {{ISBN|0387985425}}, 9780387985428, 221 pages, [James E. Gentle page 184]</ref>

[[Algebraic operation]]s work in the same way as [[arithmetic operations]],<ref>Horatio Nelson Robinson, ''New elementary algebra: containing the rudiments of science for schools and academies'', Ivison, Phinney, Blakeman, & Co., 1866, [https://books.google.com/books?id=dKZXAAAAYAAJ&dq=Elementary+algebra+notation&pg=PA7 page 7]</ref> such as [[addition]], [[subtraction]], [[multiplication]], [[Division (mathematics)|division]] and [[exponentiation]],<ref>Ron Larson, Robert Hostetler, Bruce H. Edwards, ''Algebra And Trigonometry: A Graphing Approach'', Publisher: Cengage Learning, 2007, {{ISBN|061885195X}}, 9780618851959, 1114 pages, [https://books.google.com/books?id=5iXVZHhkjAgC&dq=operations+addition%2C+subtraction%2C+multiplication%2C+division+exponentiation.&pg=PA6 page 6]</ref> and are applied to algebraic variables and terms.  Multiplication symbols are usually omitted, and implied when there is no space between two variables or terms, or when a [[coefficient]] is used. For example, <math style="margin-bottom:8px">3 \times x^2</math> is written as <math style="margin-bottom:8px">3x^2</math>, and <math>2 \times x \times y</math> may be written <math>2xy</math>.<ref>Sin Kwai Meng, Chip Wai Lung, Ng Song Beng, "Algebraic notation", in ''Mathematics Matters Secondary 1 Express Textbook'', Publisher Panpac Education Pte Ltd, {{ISBN|9812738827}}, 9789812738820, [https://books.google.com/books?id=nL5ObMmDvPEC&dq=%22Algebraic+notation%22+multiplication+omitted&pg=PR9-IA8 page 68]</ref>

Usually terms with the highest power ([[Exponentiation|exponent]]), are written on the left, for example, <math style="margin-bottom:8px">x^2</math> is written to the left of {{mvar|x}}. When a coefficient is one, it is usually omitted (e.g. <math style="margin-bottom:8px">1x^2</math> is written <math style="margin-bottom:8px">x^2</math>).<ref>David Alan Herzog, ''Teach Yourself Visually Algebra'', Publisher John Wiley & Sons, 2008, {{ISBN|0470185597}}, 9780470185599, 304 pages, [https://books.google.com/books?id=Igs6t_clf0oC&q=coefficient+of+1&pg=PA72 page 72]</ref> Likewise when the exponent (power) is one, (e.g. <math style="margin-bottom:8px">3x^1</math> is written <math style="margin-bottom:8px">3x</math>).<ref>John C. Peterson, ''Technical Mathematics With Calculus'', Publisher Cengage Learning, 2003, {{ISBN|0766861899}}, 9780766861893, 1613 pages, [https://books.google.com/books?id=PGuSDjHvircC&dq=%22when+the+exponent+is+1%22&pg=PA32 page 31]</ref> When the exponent is zero, the result is always 1 (e.g. <math style="margin-bottom:8px">x^0</math> is always rewritten to {{mvar|1}}).<ref>Jerome E. Kaufmann, Karen L. Schwitters, ''Algebra for College Students'', Publisher Cengage Learning, 2010, {{ISBN|0538733543}}, 9780538733540, 803 pages, [https://books.google.com/books?id=-AHtC0IYMhYC&q=exponents+&pg=PA222 page 222]</ref> However <math>0^0</math>, being undefined, should not appear in an expression, and care should be taken in simplifying expressions in which variables may appear in exponents.

===Alternative notation===
Other types of notation are used in algebraic expressions when the required formatting is not available, or can not be implied, such as where only letters and symbols are available. As an illustration of this, while exponents are usually formatted using superscripts, e.g., <math style="margin-bottom:8px">x^2</math>, in [[plain text]], and in the [[TeX]] mark-up language, the [[caret]] symbol {{char|^}} represents exponentiation, so <math style="margin-bottom:8px">x^2</math> is written as "x^2".<ref>Ramesh Bangia, ''Dictionary of Information Technology'', Publisher Laxmi Publications, Ltd., 2010, {{ISBN|9380298153}}, 9789380298153, [https://books.google.com/books?id=zQa5I2sHPKEC&q=exponentiation+caret&pg=PA212 page 212]</ref><ref>George Grätzer, ''First Steps in LaTeX'', Publisher Springer, 1999, {{ISBN|0817641327}}, 9780817641320, [https://books.google.com/books?id=mLdg5ZdDKToC&q=subscripts+and+superscripts+caret&pg=PA17 page 17]</ref> This also applies to some programming languages such as Lua. In programming languages such as [[Ada (programming language)|Ada]],<ref>S. Tucker Taft, Robert A. Duff, Randall L. Brukardt, Erhard Ploedereder, Pascal Leroy, ''Ada 2005 Reference Manual'', Volume 4348 of Lecture Notes in Computer Science, Publisher Springer, 2007, {{ISBN|3540693351}}, 9783540693352, [https://books.google.com/books?id=694P3YtXh-0C&q=double+star+exponentiate&pg=PA12 page 13]</ref> [[Fortran]],<ref>C. Xavier, ''Fortran 77 And Numerical Methods'', Publisher New Age International, 1994, {{ISBN|812240670X}}, 9788122406702, [https://books.google.com/books?id=WYMgF9WFty0C&dq=fortran+asterisk+exponentiation&pg=PA20 page 20]</ref> [[Perl]],<ref>Randal Schwartz, Brian Foy, Tom Phoenix, ''Learning Perl'', Publisher O'Reilly Media, Inc., 2011, {{ISBN|1449313140}}, 9781449313142, [https://books.google.com/books?id=l2IwEuRjeNwC&q=double+asterisk+exponentiation&pg=PA24 page 24]</ref> [[Python (programming language)|Python]]<ref>Matthew A. Telles, ''Python Power!: The Comprehensive Guide'', Publisher Course Technology PTR, 2008, {{ISBN|1598631586}}, 9781598631586, [https://books.google.com/books?id=754knV_fyf8C&q=double+asterisk+exponentiation&pg=PA46 page 46]</ref> and [[Ruby (programming language)|Ruby]],<ref>Kevin C. Baird, ''Ruby by Example: Concepts and Code'', Publisher No Starch Press, 2007, {{ISBN|1593271484}}, 9781593271480, [https://books.google.com/books?id=kq2dBNdAl3IC&q=double+asterisk+exponentiation&pg=PA72 page 72]</ref> a double asterisk is used, so <math style="margin-bottom:8px">x^2</math> is written as "x**2". Many programming languages and calculators use a single asterisk to represent the multiplication symbol,<ref>William P. Berlinghoff, Fernando Q. Gouvêa, ''Math through the Ages: A Gentle History for Teachers and Others'', Publisher MAA, 2004, {{ISBN|0883857367}}, 9780883857366, [https://books.google.com/books?id=JAXNVaPt7uQC&dq=calculator+asterisk+multiplication&pg=PA75 page 75]</ref> and it must be explicitly used, for example, <math style="margin-bottom:8px">3x</math> is written "3*x".