How do I evaluate the PV term when calculating a change in enthalpy?

As we know enthalpy is defined by the equation $H = E+PV$.


Now to calculate this $PV$ factor for $\Delta H$, Sometime we take $P \Delta V$ and sometime $P\_2V\_2-P\_1V\_1$. Why are there so many different approaches? 


I am also confused whether $P$ is external pressure or internal pressure.




The derivation for $\Delta H$ is 
$$H = U + PV$$
$$\Delta H = \Delta U + \Delta (PV)$$


The $\Delta (PV)$ term expands to your $P\_2 V\_2 - P\_1 V\_1$ term. However, when the pressure is constant $P\_2 = P\_1 = P$, and $\Delta (PV)$ term becomes $P\Delta V$. The most common situation when the latter is true is when the system is open to the atmosphere and $P$ is the external pressure. In the former case, $P$ is more likely the internal pressure, which changes during the reaction. 


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