Final answer:
Stars like the Sun expand onto the giant branch during their evolution, which is the final phase before becoming a white dwarf.
Step-by-step explanation:
During the evolution of a star like the Sun, it starts off in the main-sequence phase where it fuses hydrogen to form helium. As it ages, the star evolves away from the main sequence and expands to become a red giant or supergiant. The expansion onto the giant branch occurs as a result of hydrogen fusion in a shell outside the core. This phase is the final phase of a star's life cycle before it becomes a white dwarf.