def parse_term(term):
    """Parse a single term like '3*x^2'."""
    term = term.replace(" ", "")  # Remove any spaces
    if '*' in term:
        coeff_part, var_part = term.split('*')
    else:
        if 'x' in term:
            if term.startswith('-'):
                coeff_part, var_part = term[0:2], term[2:]
            else:
                coeff_part, var_part = term.split('x')
                var_part = 'x' + var_part
        else:
            coeff_part, var_part = term, ''
    
    if '^' in var_part:
        var, power = var_part.split('^')
    else:
        var = var_part
        power = '1' if var_part else '0'
    
    coeff = int(coeff_part) if coeff_part not in ["", "-", "+"] else -1 if coeff_part == "-" else 1
    power = int(power)
    
    return (coeff, var, power)

def parse_expression(expr):
    """Parse an expression like '3*x^2 + 2*x - 1' into terms."""
    terms = []
    term = ''
    for char in expr:
        if char in '+-' and term:
            terms.append(term)
            term = char
        else:
            term += char
    terms.append(term)
    
    return [parse_term(term) for term in terms]

def expand(expr1, expr2):
    """Expand the product of two expressions."""
    terms1 = parse_expression(expr1)
    terms2 = parse_expression(expr2)
    
    result = {}
    
    for (c1, v1, p1) in terms1:
        for (c2, v2, p2) in terms2:
            if v1 == v2 or v1 == '' or v2 == '':
                var = v1 if v1 else v2
                power = p1 + p2
                coeff = c1 * c2
                if (var, power) in result:
                    result[(var, power)] += coeff
                else:
                    result[(var, power)] = coeff
    
    return result

def format_expression(terms):
    """Format the terms into a string expression."""
    formatted_terms = []
    for (var, power), coeff in sorted(terms.items(), key=lambda x: -x[1]):
        if power == 0:
            formatted_terms.append('{}{}'.format('+' if coeff >= 0 else '', coeff))
        elif power == 1:
            formatted_terms.append('{}{}*{}'.format('+' if coeff >= 0 else '', coeff, var))
        else:
            formatted_terms.append('{}{}*{}^{}'.format('+' if coeff >= 0 else '', coeff, var, power))
    return ' '.join(formatted_terms).replace('+ ', '+').replace('- ', '-')

def main():
    expr_input1 = input("Saisissez la première\nexpression algébrique\n(par exemple, x+1): ")
    expr_input2 = input("Saisissez la deuxième\nexpression algébrique\n(par exemple, x-2): ")
    
    # Normaliser les expressions saisies
    expr_input1 = expr_input1.replace("-", "- ")
    expr_input2 = expr_input2.replace("-", "- ")
    
    expanded_terms = expand(expr_input1, expr_input2)
    expanded_expr = format_expression(expanded_terms)
    
    print("Expression développée :\n{}".format(expanded_expr))

main()