Final answer:
The core of a star expands due to increased energy production from hydrogen fusion occurring in a shell around the helium core, which generates heat and causes the outer layers to expand.
Step-by-step explanation:
The expansion of a star's core is primarily caused by the increase in energy production during the fusion process. When hydrogen in the core of a main sequence star is exhausted, the core contracts under gravity and heats up. This increased temperature causes hydrogen fusion to commence in a shell around the helium core. The production of new energy from this fusion process generates additional heat, which then causes the outer layers of the star to expand. Ultimately, the core expands due to this process, where the balance between the inward force of gravity and the outward pressure from thermal gas - the former trying to contract the star and the latter trying to expand it - is readjusted, resulting in an enlarged star.