Tool to realize the development of a mathematical expression (polynomial, product, etc.), this expansion is the reverse of the factoring process, and it create an expanded form.

Math Expression Expansion - dCode

Tag(s) : Symbolic Computation

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The development consists of the decomposition/transformation of a multiplication or a mathematical product into a sum (or a difference).

The development is also called an *expansion*.

To achieve the operations, dCode uses the distributive property of multiplication over addition and subtraction.

The concept of *distributivity* is the most important for expanding: $ a \times (b + c) = (a \times b) + (a \times c) $

__Example:__ $ (a+b)^2 $ is expanded $ a^2+2ab+b^2 $

Indicate directly the polynomial (with or without $ = 0 $) in the box.

Developing a math expression (or a part of an equation) consists in expressing it in sum of factors (to eliminate the possible factorization) in order to obtain a longer writing but which can then make it possible to carry out simplifications. This technique is called a polynomial expansion. After expansion, the dCode calculator automatically computes the reduced form of the algebraic expression.

The principle is identical with the trigonometric functions (functions sine, cosine, etc.) and some of their distributivity properties in order to simplify their content

__Example:__ $ \sin(2x) $ gives $ 2\sin(x)\cos(x) $

dCode retains ownership of the "Math Expression Expansion" source code. Except explicit open source licence (indicated Creative Commons / free), the "Math Expression Expansion" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Math Expression Expansion" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Math Expression Expansion" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

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Cite as source (bibliography):

*Math Expression Expansion* on dCode.fr [online website], retrieved on 2024-09-14,

expansion,polynomial,expression,math,decomposition,expand,product,sum,development,distributivity

https://www.dcode.fr/math-expression-expand

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