Vhdl Alu

It is possible to create an ALU that add, subtracts and multiplies all in one? I cannot seem to get the multiplication to work because I need double the storage because the numbers are being multiplied. Do I just need to use different storage variables? Is there a "cleaner" way?

library ieee;
use ieee.std_logic_1164.all;
use ieee.std_logic_unsigned.all;
use ieee.std_logic_arith.all;
ENTITY ALU IS
    port(x, y : in std_logic_vector(7 downto 0);    --variables on which opeation is performed
        operation : in std_logic_vector(2 downto 0); --how to choose what operation
        zero : out std_logic;
        result : out std_logic_vector(7 downto 0));
END ALU;
architecture ALU_ARCH  of ALU is
begin
    process(operation)
    variable temp: std_logic_vector(7 downto 0);
    begin
    case operation is
        when "101" =>
            temp := x + y;
        when "110" =>
            temp := x - y;
        when "111" =>
           temp:=x*y;
        when others =>
            temp := x - y;
    end case;
    
    result <= temp;
    end process;
end ALU_ARCH;