Let's match each term with its corresponding descriptive elements
Conquest
- fast
- less assimilation of local culture
- higher risk of resistance from potential converts
When Islam was spread by conquering other territories, the process was fast and encountered opposition by the population of those territories. In those conquests, muslims did not have any interest on local culture, they just exercised their dominance and imposed their culture over the territories acquired.
Trade
- slow
- more assimilation of local culture
- lower risk of resistance from potential converts
When a culture is spread through the establishment of trade relationships with another, these bonds are generally sustained by long lasting agreements which require getting to know the other party and assimilating its practices. Such manner of spreading a religion usually encounters no resistance as trade agreements take place when both parties are obtaining a profit from it, and none of them would be reluctant.