# 4.3 Expressions and Equations: How Maple "thinks"

Your calculator can calculate with numbers. Maple can calculate with unknown quantities; that is, variables. For example:
```> x+z;

x + z

> " ^ 6;

6
(x + z)
```
Notice the double quote mark ("). It always stands for the previous expression; so above, it stands for x+z.

Continuing the example:

```> expand( " );

6      5         4  2       3  3       2  4        5    6
x  + 6 x  z + 15 x  z  + 20 x  z  + 15 x  z  + 6 x z  + z
```

The built-in function expand knows how to expand an algebraic expression (i.e. multiply out all the terms in parentheses).

Conversely, Maple knows how to factor algebraic expressions:

```> factor(");

6
(x + z)
```

Another useful function that can be applied to any expression is simplify(), which applies various known algebraic and trig identities to try and simplify an expression:

```> sin(x)^2 + 3 * cos(x)^2;

2           2
sin(x)  + 3 cos(x)

> simplify(");

2
2 cos(x)  + 1
```

Keith Orpen, who is still writing this, would like to hear your comments and suggestions.