How did the federal government promoted westward expansion in a
variety of ways.

The Federal government responded with measures (Homestead Act, transcontinental railroad) and military campaigns designed to encourage settlement, solidify Union control of the trans-Mississippi West, and further marginalize the physical and cultural presence of tribes native to the West.

the ones that are losing there jobs

an expansion is one of two basic business cycle phases; the other is contraction. the transition from expansion to contraction is a peak, and the changeover from contraction to expansion is a trough.