sed provide regular expression as shell variables code example

Example 1: sed replace with variable

Just concatenate var '"$var"' to replace values string in sed command:
$ sed -i 's/string_to_replace/'"$var"'/g' file_to_replace.txt

Example 2: sed replace with variable

For using match in sed replacement, just border it with '\(' and '\)':
echo Before123 | sed 's/Before\([0-9]*\)/\1After/g'
123After	# number is matched withtin '\( \)' and replaced in '\1'
Example with 2 match replacements
echo a_b | sed 's/\(^.*\)_\(.*$\)/first is \1 and \2 is after/g'