$re = '/([a-z]+)\*\1(?=[^#]*#[^#]*(?:[^#]*#[^#]*#[^#]*)*$)/';
$str = 'As a 1st step, you can rewrite #21x*x - 1y = 1z + 1#. But what about the 2nd #3x + 1y = 1z#?';
$subst = "$1^2";
$result = preg_replace($re, $subst, $str);
echo "The result of the substitution is ".$result;
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php