Why are c4 and cam photosynthesis more energetically expen- sive than c3 photosynthesis? what climate conditions would favor c4 and cam plants?

This is because  these plants (C4 and CAM) needed to avoid the wasteful process  of PHOTORESPIRATION.; by first  producing C4 -malate , and oxaloacetate compound,s   before  the usual  C3 compunds GLYCERATE PHOSPAHTE is produced (after decaboxylation),  to enter  CALVIN cylce.

The name C3  and C4 comes from the number of carbon compounds produced -the first compound MALATE in  C4 pants is a 4 carbon compound , and first  3C  compoud GLYCERATEPHOPAHTE  produced in  C3 Plants.

Explanation:

C3 plants usually  reduce C02 by reaction with RIBULOSE BIPHOSPAHTE;the reaction is catalysed  by enzyme  RUBISCO (most abundant enzymes in the world) to produce 6 carbon intermediate which splits to 2 molecules of three carbon compounds  GLYCERIDE - 3-PHOPHATE (GP)

GP is reduced  to 3Carbon  sugar Triphosphate  in the presence of ATP and NADP from light dependent stage,  The Triphospahte  is converted to glucose, Amino acids  and Lipids.

However, C4 plants e.g maize , shorghum  which grow in tropics, of high temperature and high light intensities with low altitudes usually  face difficulties with enzyme RUBISCO, beacuse the  enzymes can catalyse   both the reaction of CO2 with Ribulose biphosphate and  that of Oxygen with  the same compound.

This competitive inhibition  reduce the availability of Ribulose biphospahte for CO2 and therefore Carbohydrate production.

To avoid this the C4 plants  have special adaptations that shunt Oxygen from the atmosphere.They have special mesophyll cells with direct contact with atmosphere. Phosphoenol pyruvate (PEP) is present in the mesophyll cells . C02 combined with PEP , a reaction catalysed by enzyme PEPcaboxylase; to form OXALOACATATE,(4C) compounds. The latter is converted to Malate. The malate is pass  into the Bundle sheath where enzynme RUBISCO is located,

The malate is decaboxylated (removal of C02). The available is C02 reacts  Ribulosebiphosphate in the presence of Rubisco in the normal C3   fashion to form TP.

SUMMARY

30 ATPs ARE NEEDED TO PRODUCE 1 MOLECULE OF GLUCOSE BY C4 PLANTS , WHILE 18ATPS ARE NEEDED TO PRODUCE THE SAME MOLECULE OF GLUCOSE  BY C3 PLANTS.

These C4 process  required additional STEPS and  ENERGY(ATPs), and  therefore more expensive than C3 steps.