To put it into context. Did European powers start with trade and gradually seep into politics and eventually colonize a country under the native Africans noses, or was did they march in with X number of troops, shoot/capture the chieftain and take over?
It was just swift takeovers. In 1870 only 10% of Africa was colonised, a few small Portuguese, French and British holdings, with a large Ottoman holding in the northeast.
By 1880 it was about 25% of Africa that had been colonised.
At the turn of the century only 10% was independent. France controlled basically all northwest Africa, the UK controlled a strip from southern Africa to the north and northwest. The Belgians established a large central African colony under which they killed one half of the population in about 20 years.
The Battle of Omdurman basically sums up how colonisation was so quick. The British put up an army of 25, 000 against an army of over 50, 000
The British saw less than 500 deaths, whilst the Sudanese saw over 10, 000. European expansion was industrial against a relatively primitive continent. And there was also the fact that even when done "legally" they have chieftains sign over territories in languages drawn up in languages they didn't understand.