How to use Pascal's triangle for binomial expansion

The question is asking for me to expand ${(p+r)}^4$. I know that I have to use Pascal's triangle, the fourth set down, which is $1,4,6$,$4,1.$ My thinking is that I have to use these numbers to solve this through synthetic division, but don't really know what to do from there. Please let me know if I'm completely wrong.

It's simpler than that. The $1,4,6,4,1$ tell you the coefficents of the $p^4$, $p^3r$, $p^2r^2$, $pr^3$ and $r^4$ terms respectively, so the expansion is just
$$1p^4 + 4p^3r + 6p^2r^2 + 4pr^3 + 1r^4$$
$$p^4 + 4p^3r + 6p^2r^2 + 4pr^3 + r^4$$
• Bonus exercise for the OP: figure out why this works by starting with the constant polynomial $1$ and repeatedly multiplying it by $(p+r)$. Compare this with the way you calculate the numbers in Pascal's triangle. Nov 19, 2015 at 19:50