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Math Expression Expansion

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.

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

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

### How to expand a trigonometric 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 $2\sin(x)\cos(x)$

## Source code

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Math Expression Expansion on dCode.fr [online website], retrieved on 2024-09-14, https://www.dcode.fr/math-expression-expand

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