# If you'd like to omit non-matching lines from the result; add ';d' to the end of the expression.
sed -E 's/([a-z]+)\*\1(?=[^#]*#[^#]*(?:[^#]*#[^#]*#[^#]*)*$)/$1^2/g;t' <<< "As a 1st step, you can rewrite #21x*x - 1y = 1z + 1#. But what about the 2nd #3x + 1y = 1z#?"
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 SED, please visit: https://www.gnu.org/software/sed/manual/html_node/The-_0022s_0022-Command.html