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Math Expression Expansion

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

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Math Expression Expansion -

Tag(s) : Symbolic Computation

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# Math Expression Expansion

## Trigonometric Expression Expansion

### What does expand an expression means? (Definition)

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 developping: $a \times (b + c) = (a \times b) + (a \times c)$

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

### How to develop a polynomial-like expression?

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, dCode calculator automatically computes the reduced form of the math expression.

### How to expand a trigonometric expression?

dCode expands algebraic expressions but also trigonometric expressions (functions sine, cosine, etc.) in order to simplify their content

Example: $\sin(2x)$ gives $2\sin(x)\cos(x)$

## Source code

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, 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, tablet, iPhone or Android !
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