# Multiply polynomials and expand expressions (online calculator)

The command pe expands a polynomial. Input the command pe and polynomial you want to expand in the header form as follows.

pe (3*x+5)**2


In this case, (3*x+5)**2 is the polynomial meaning

$\left(3 x + 5\right)^{2}$

and the result is

$9 x^{2} + 30 x + 25$

The calculator can't recognize the implicit multiplication (2x, 3x, etc) so you should write 3*x instead of 3x. Double asterisks (**) means the power.

## Expand third degree polynomials

You can expand polynomials of degree three such as 2*(x-1)**3.

pe 2*(x-1)**3


It means

$2 \left(x - 1\right)^{3}$

and the output is

$2 x^{3} - 6 x^{2} + 6 x - 2$

It's difficult and takes too long to expand high degree polynomials so let's use this online calculator. The result screen is like this. ## Multiply polynomials

The pe command enables you to multiply polynomials.

pe (x-1)*(x+2)


This means multiply (x-1) and (x+2), that is

$\left(x - 1\right) \left(x + 2\right)$

The output is

$x^{2} + x - 2$

## Euler number and pi

If the polynomials have the Euler number or pi, use E and pi respectively.

pe E*(x-sin(pi/2))**2


It means this.

$e \left(x - 1\right)^{2}$

The E means Euler number e (=2.71828...). There is no sin and pi symbols in the expression because the program automatically simplifies sin(pi/2) before expanding the polynomial. The output of above expression is

$e x^{2} - 2 e x + e$

## Note

The process of expanding an algebraic expression or multiplying polynomials is severe so it may take several seconds to output in the screen.