algebra.pl

@a=map{[split'\+|(?=-)']}    # Split each factor into components
    <>=~s/\n//r=~s/(\(.+?\))\^(\d)/$1x$2/ger=~/[^()]+/g;    # Get factors by flattening exponents then splitting list on parenthesized expressions
for(@{$a[0]}){
    $l{/\d/?'':$_}=/\d/?$_:1    # Initialize %l (hash from variable to coefficient) with first factor
}
for(1..$#a){    # Loop through other factors to multiply
    %b=();    # Temporary hash to store current result in
    for(@{$a[$_]}){    # Loop $_ through components of current factor
        while(($k,$v)=each%l){ # Loop $k,$v through variables and coefficients of current polynomial
            $b{/\d/?$k:join'',sort($_,split'',$k)}+=/\d/?$v*$_:$v # If component is a number multiply coefficients by it, otherwise append it to variables (and sort to keep unique indexes)
        }
    }
    %l=%b # Set current polynomial to temporary result
}
print(
    (join' ',map{"$l{$_}$_"}sort{length$b<=>length$a}keys%l) # Format hash as list ordered by degree
    =~s/\b1(?=[a-z])//gr=~s/-/- /gr=~s/\b \b/ + /gr=~s/(([a-z])\2+)/"$2^".length$1/gre) # String substitutions to do the rest of the formatting