After the defeat of Russia, Japan focused on the expansion of its empire, beginning with

seizing Manchuria and eventually annexing it.

seizing the Korean peninsula and eventually annexing it.

seizing the Philippines as a protectorate.

seizing the island of Formosa as a protectorate.

After the defeat of Russia, Japan focused on the expansion of its empire, beginning with seizing the Philippines as a protectorate.

I believe the answer is: seizing the Korean peninsula and eventually annexing it.

The purpose of obtaining Korean peninsula was because it's a strategic location which allow japan to control the trade toward the central ans western Asia region. This area was finally annexed after the Japan-Korea Treaty which established in 1910