What did the motives of Germany, Italy, and Japan have in common
I think you are referring to the WWII era when all three of these nations made up the Axis Powers. One major thing that they had in common was that the leaders of all three nations felt disrespected by the peace process which ended WWI. Japan's claims in the Pacific were not honored and the Western imperial powers still maintained colonies there. Germany was blamed for WWI and had to pay back billions in reparations to the Allies all while losing major industrial centers. The Entente promised Italy some territory from the Austro-Hungarian Empire if it would join their side in WWI, but this land never materialized.
Another thing that these nations had in common during WWII was that their leadership was taken over by pro-military strongmen who wanted to expand national borders. Hitler went against the disarmament portion of the Versailles Treaty by building up the infantry and air force arms of the German military. Benito Mussolini desired to re-create the old Roman Empire and turn the Mediterranean into a Roman lake once again. Japan sought to make itself the strongest nation in Asia by using its neighbors for raw materials and slave labor. By embracing militarism and expansion, all three of these nations hoped to gain the respect that they felt was not given to them at Versailles.