# 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.