### Using symbolic computation

The main feature of Maple is symbolic computation.  In other words, Maple does algebra. Here are some examples.

Example

Output

(x + y)^2;

(x + y)2

A basic expression.
k := x*y - y^2;

k := xy + y2

k is now an alias for the expression.  Note that k is simply another name for the expression - they are not equal in the mathematical sense.
p := k /(x-y);   You can now use k to refer to the expression.  Maple immediately substitutes the value of k.
k := 'k';

k

You can unassign a variable by assigning it to its own name in single quotes.
simplify(p);

y

The simplify command does algebraic simplification.
p := x^2 - 8*x +15; p := x2 - 8x  + 15 Maple doesn't mind if you re-use names.  The old value is lost.
solve(p=3,x);

2,6

Use the solve command to solve equations.  Note the use of the = sign.  Here, it is used in a mathematical sense.  Maple will try different values for x until it finds all of them that make the mathematical statement x2 - 8x  + 15 = 3 true.
dpdx := diff(p,x);

dpdx := 2x - 8

The diff command differentiates an expression with respect to a variable.
int(p,x);   The int command integrates an expression.  Note that the constant of integration is left off.
subs(x=4,p);
subs(x=t^2,p);

-1
t4 - 8t2 + 15

The subs command substitutes expressions into other expressions.  Notice that p's value is unchanged.

Each of the commands listed here has many powerful, advanced features.  See the help files for more information.
Use the restart; command to unassign all variables, reset built-in variables (such as Digits) to their original values, and unload all packages. Of course, this should be used with care.