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.

Expand third polynomials

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

\[ e x^{2} - 2 e x + e \]


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