To be able to successfully and easily expand your paragraphs, you want to be sure that your paragraphs are addressing some thesis about politics in the 1960s or some underlying topic concerning politics in the 1960s. Based on the image you included below, it seems likely your overall essay topic may concern the Civil Rights Movement of the 1960s. Hence, if you focus your research on the presidents of the 1960s to see exactly how they did and did not contribute to the Civil Rights Movement, then you'll very easily find enough to say to expand your paragraphs. Based on your query, it's most likely that you want to focus on writing about the following three president: (1) President Dwight D. Eisenhower, in office from 1953 to 1961; (2) President John F. Kennedy, in office from 1961 to 1963; and (3) President Lyndon B. Johnson in office from 1963 to 1969.
Particularly interesting facts about Eisenhower concern his actions towards racial segregation and African-American disfranchisement. Eisenhower was president when The Supreme Court ruled in 1954 that racial segregation in public schools was unconstitutional as a result of the Brown vs. Board of Education of Topeka case (American President: A Reference Resource, "Dwight David Eisenhower").
As president, he needed to uphold the Court's decision and ran into conflict with Governor Orval Faubus of Arkansas. Faubus made the personal decision to use the National Guard to block African Americans from enrolling in Central High in Little Rock but backed down when Eisenhower had a discussion with him about the Constitutional necessity to uphold the Court's decision; however, Faubus also withdrew the National Guard, which only led to mob violence and Eisenhower's need to send federal troops into Little Rock, the first time a president has had to send federal troops into the South to uphold federal law since the Reconstruction ("Dwight David Eisenhower").
Eisenhower was also the first to sign civil rights legislation since the Reconstruction by signing the Civil Rights Act of 1957 to try to eliminate restrictions the South had placed on African-American voting rights, such as "literacy tests, poll taxes, and other obstacles"; however, Southern Democrats modified the bill to require a jury to judge if an African-American citizen's voting rights had been infringed upon ("Dwight David Eisenhower").
John F. Kennedy sought to make more significant civil rights changes than Eisenhower but was sadly assassinated before any official legislation could be made. President Lyndon B. Johnson promised to pick up where Kennedy left off and signed the Civil Rights Act of 1964 ("Lyndon B. Johnson and Civil Rights").