How did the advent of cotton factories shape American economic trends?
When you talk about "cotton factories," I assume you are referring to textile factories like the ones at Lowell, MA. The creation of these factories did not, by themselves, change the US economy. However, they were the first steps in industrialization and industrialization was a huge influence on economic trends in the US.
The major change that came with industrialization was that workers really lost control of their labor and the fruits of that labor. Before the factories were created, much of the work of America was done in people's homes by families and perhaps a few apprentices and other helpers. The work was relatively skilled and a large percentage of artisans were or could expect to become their own bosses.
As industrialization continued, however, work became something that was relatively unskilled and was done outside the home. Instead of becoming a cobbler and making shoes, a person might become a worker in a shoe factory, working when they were told to work and not doing anything that required great skill. This was a major economic trend that came about after the textile factories started the US towards industrialization.