How to use Pascal's triangle for binomial expansion

Question

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.

Answer 1

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

$$ 1p^4 + 4p^3r + 6p^2r^2 + 4pr^3 + 1r^4 $$

so

$$ p^4 + 4p^3r + 6p^2r^2 + 4pr^3 + r^4 $$