I want to use PHP to calculate simple algebraic expressions like, 8*(5+1), entered via an tag by a normal user (which means,
I'd start by stripping the input of anything which shouldn't be in the expression (assuming you just want to allow add, subtract, multiply, divide, and no variables):
$expr = preg_replace('/[^0-9+*\/-]/', '', $expr);
and then, once I'm confident nothing dangerous remains in the user input, simply pass the itthrough eval() to evaluate the expression:
$result = eval("return $expr;");
No need to reinvent the wheel.
Edited to incorporate Kolink's corrections. Thanks!