Calculator is able to expand an algebraic expression online and remove unnecessary brackets.

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 expansion calculator 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 expansion calculator 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`.

expand(expression), expression is expression algebraic to expand.

Here somes examples of using the computer to expand algebraic expression:

- 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

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- Trigonometric Calculator : simplify_trig. Calculator wich uses trigonometric formula to simplify trigonometric expression.
- List of calculations applicable to an algebraic expression : see_possible_calculations. Return the list of calculations that can be done on an algebraic expression.
- Calculation of binomial coefficients : binomial_coefficient. A binomial coefficient calculator that allows you to calculate a binomial coefficient from two integers.
- Partial fraction decomposition calculator : partial_fraction_decomposition. The calculator allows a rational fraction to be broken down into simple elements.
- Derivative calculator : derivative. The derivative calculator allows steps by steps calculation of the derivative of a function with respect to a variable.
- Taylor expansion calculator : taylor_series_expansion. The taylor series calculator allows to calculate the Taylor expansion of a function.
- Logarithmic expansion : expand_log. The calculator makes it possible to obtain the logarithmic expansion of an expression.
- Trigonometric expansion : expand_trigo. The calculator makes it possible to obtain the trigonometric expansion of an expression.
- Expand calculator : expand. Calculator is able to expand an algebraic expression online and remove unnecessary brackets.
- Expand and simplify an algebraic expression online : expand_and_simplify. Online calculator that allows you to expand and reduce an algebraic expression.
- Factoring calculator : factor. The factoring calculator allows to factor an algebraic expression online with steps.
- Solved mathematical exercises generator : exercise_generator. Returns a list of mathematical exercise statements and their solutions that can be used by teachers to prepare tests and quizzes.
- Integral calculator : integral. The integral calculator calculates online the integral of a function between two values, the result is given in exact or approximated form.
- Indefinite integral calculator : antiderivative. The antiderivative calculator allows to calculate an antiderivative online with detail and calculation steps.
- Limit calculator : limit. 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.
- Calculation of the monthly payments of a loan : monthly_loan. Loan monthly payment calculator : home loan, consumer loan, and other types of loan.
- Scientific online calculator : evaluate. Online Scientific Calculator to calculate algebraic expressions and get a numerical result.
- Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.