what type of chemical reactions are these?

1)
2Fe₂O₃ + 3C → 4Fe + 3CO₂ …. double decomposition / reduction

2)
2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O …. combustion / oxidation

3)
2P₂ + 5O₅ → 2P₂O₅ …. synthesis / oxidation

4)
2Al₂O₃ → 4Al + 3O₂ …. decomposition

Reaction types......

1) 2Fe2O3 + 3C --> 4Fe + 3CO2 ................ single replacement
2) 2C2H6 + 7O2 --> 4CO2 + 6H2O ............. complete combustion of a hydrocarbon
3) 2P2 + 5O2 --> 2P2O5 .............. .............. synthesis (or combination)
4) 2Al2O3 --> 4Al + 3O2 ............. ............... decomposition (if it occurred *)

There are some easy clues for identifying simple reactions.
Synthesis (combination) -- single product
Decomposition -- single reactant
Single replacement -- element + compound gives element + compound
Double replacement -- two compounds on each side, where at least one product is insoluble (precipitates) or the reaction is an Arrhenius acid/base reaction.
Complete combustion of a hydrocarbon -- produces CO2 and water vapor, but only the "complete" reaction for the burning of a hydrocarbon. Be sure you write the whole phrase. Note: there are other kinds of "combustion." Iron burning in oxygen to make Fe2O3 is "combustion", but it doesn't make CO2 and H2O. --- 4Fe(s) + 3O2(g) --> 2Fe2O3(s). The reaction is classified as "synthesis", not "combustion."

Take a look at my website:
https://c7chemistry.wikispaces.com/file/view/Reactions%20Table%20011712.pdf/303163824/Reactions%20Table%20011712.pdf
https://c7chemistry.wikispaces.com/file/view/CW%20reaction%20id%20and%20completion%20050906.pdf/626230409/CW%20reaction%20id%20and%20completion%20050906.pdf

* Aluminum oxide does not just "fall apart." It is a very difficult compound to decompose and requires lots of heat and electricity to electrolyze the molten alumina (Al2O3).