Final answer:
African American politicians were able to make a lasting difference by helping write new state constitutions after the Civil War.
Step-by-step explanation:
African American politicians serving in state governments after the Civil War were able to make a lasting difference by helping write new state constitutions. These state constitutions established important reforms such as the establishment of public school systems and the opening of state institutions to both black and white residents. By actively participating in revising state constitutions, African American politicians played a crucial role in shaping the post-Civil War South.