How do you expand (p+q)^5?

Jan 17, 2017

${p}^{5} + 5 {p}^{4} q + 10 {p}^{3} {q}^{2} + 10 {p}^{2} {q}^{3} + 5 p {q}^{4} + {q}^{5}$

Explanation:

Write out Pascal's triangle to the the fifth line or memorize the first few lines:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Then write out the $p$'s and $q$'s with the powers going in opposite directions. Make sure that the index of $p$ plus the index of $q$ in each term add up to $5$.