Extracting a metal from its ore is a reduction: the metal in the ore must lose its oxygen, or its ions must gain electrons. The method chosen depends on where the metal sits in the reactivity series and on how much the process costs.
A metal that is less reactive than carbon can be extracted by heating with carbon. The carbon takes the oxygen from the metal oxide, so the oxide is reduced and the carbon is oxidised. Iron is made this way: 2Fe2O3 + 3C → 4Fe + 3CO2. It is cheap because carbon is cheap and the process only needs heat.
A metal that is more reactive than carbon holds on to its oxygen too strongly, so carbon cannot remove it. These metals are extracted by electrolysis of a molten compound. Aluminium is extracted by electrolysis of aluminium oxide dissolved in molten cryolite. Electrolysis is expensive because it needs large amounts of electricity and the compound has to be kept molten.
