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

- Indefinite integral calculator : antiderivative_calculator. The antiderivative calculator allows to calculate an antiderivative online with detail and calculation steps.
- 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.
- Algebra calculator : calculator. Calculator that allows to make algebraic calculation by combining operations with letters and numbers, and to indicate the steps of calculation
- Find the derivative of a function : derivative_calculator. The derivative calculator allows steps by steps calculation of the derivative of a function with respect to a variable.
- 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.
- Integral calculator : integral_calculator. The integral calculator calculates online the integral of a function between two values, the result is given in exact or approximated form.
- Limit of a function : limit_calculator. The limit calculator allows the calculation of the limit of a function with the detail and the calculation steps.
- Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
- Partial fraction decomposition : partial_fraction_decomposition. The calculator allows a rational fraction to be broken down into simple elements.
- Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
- Calculate the Taylor expansion of a function : taylor_series_expansion. The taylor series calculator allows to calculate the Taylor expansion of a function.
- Trigonometric Calculator : trig_calculator. Calculator wich uses trigonometric formula to simplify trigonometric expression.

Algebraic calculation