Final answer:
Louis Botha and Jan Smuts supported the British in World War I due to economic interests, national unity, and the strategic importance of remaining aligned with the British Empire, despite past conflicts during the Boer Wars.
Step-by-step explanation:
Louis Botha and Jan Smuts wanted to support the British and enter World War I on the side of the British due to a variety of reasons. Firstly, the Boer Wars (1880-81 and 1899-1902) had severely strained the relationship between the Boer Republics and Britain, but also led to a reconciliation when the Union of South Africa was formed in 1910, with Botha as its first Prime Minister and Smuts as a key minister. Despite their past conflicts, Botha and Smuts saw alignment with Britain as beneficial to the Union of South Africa's international standing and economic interests - particularly regarding South Africa's mineral resources and the strategic importance of the British Empire's support against hostile neighbors and internal challenges.
Additionally, the global context of the time idealized national unity and cohesion against a common external enemy, personified by the Central Powers. Botha and Smuts also likely recognized the potential for gaining or solidifying political power within the British Empire and ensuring their dominion's strategic and economic interests were protected. Their decision underscored the complexity of colonial politics and the shifting allegiances that characterized the early 20th century.