Calculator is able to expand an algebraic expression online.

expand online

In mathematics, to **expand an expression** or to **expand a product**
that is transformed into algebraic sum. This **calculator allows to expand** all forms of **algebraic
expressions online**, it also helps to calculate special expansions online (the difference of squares,
the identitiy for the square of a sum and the identity for the square of a difference).
For simple expansions, the calculator gives the calculation steps.

the function allows to expand online all forms of mathematical expressions, the expression can be alphanumeric, ie it can contain numbers and letters :

- Expand the following product (3 x+ 1) (2 x+ 4) `(3x+1)(2x+4)` returns `3*x*2*x+3*x*4+2*x+4`
- Expand this algebraic expression `(x+2)^3` returns `2^3+3*x*2^2+3*2*x^2+x^3`

The function expand makes it possible to **expand a product**, it applies to all mathematical expressions,
especially the following identities :

- the identitiy for the square of a sum : It allows to expand online expressions of the form `(a+b)^2`
- the identity for the square of a difference : It allows to expand online expressions of the form `(a-b)^2`
- the difference of squares : It allows to expand online expressions of the form `(a-b)(a+b)`

**Newton's binomial formula** is written : `(a+b)^n=sum_(k=0)^{n} ((n),(k)) a^k*b^(n-k)`.
The numbers `((n),(k))` are the binomial coefficients,
they are calculated using the following formula : `((n),(k))=(n!)/(k!(n-k)!)`.

We note, that by replacing n by 2, we can find remarkable identities.

The calculator uses Newton's formula to develop expressions of the form `(a+b)^n`.

The calculator allows you to expand and collapse an expression online,
to achieve this, the calculator combines the functions collapse and expand.
For example it is possible to expand and reduce
the **expression** following `(3x+1)(2x+4)`, The calculator will returns the expression in two forms :

- expanded expression `3*x*2*x+3*x*4+2*x+4`
- expanded and reduced expression `4+14*x+6*x^2`.

Calculator is able to expand an algebraic expression online.

- expand(`(3+4)*2`) returns 3*2+4*2
- expand(`x*(x+2)`) returns x*x +x*2
- expand(`(x+3)^2`) returns `3^2+2*3*x+x^2`

See also :

- Calculation of binomial coefficients : binomial_coefficient. A binomial coefficient calculator that allows you to calculate a binomial coefficient from two integers.
- Scientific online calculator : calc. Online Scientific Calculator to calculate algebraic expressions and get a numerical result.
- Expand calculator : expand. Calculator is able to expand an algebraic expression online.
- Expand and simplify an algebraic expression online : expand_and_simplify. The online calculator function to expand and collapse an algebraic expression.
- Factoring calculator : factoring_calculator. The factoring calculator allows to factor an algebraic expression online with steps.
- Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
- Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
- Trigonometric Calculator : trig_calculator. Calculator wich uses trigonometric formula to simplify trigonometric expression.