# expand calculator

## Calculus expand

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### Function : expand

#### Summary :

Calculator is able to expand an algebraic expression online.

Expand online

#### Description :

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.

## Expand algebraic expressions

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
Note that the result is not returned as the simplest expression in order to be able to follow the steps of calculations. To simplify the results, simply use the reduce function.

## Special expansions online

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)

## Use of Newton's binomial formula

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.

## Expand and simplify an expression

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.

#### Syntax :

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

#### Examples :

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

Calculate online with expand (expand calculator)