  We provide estimates for sums of the form \[\left|\sum_{a\in A}\sum_{b\in
B}\sum_{c\in C}\chi(a+b+c)\right|\] and \[\left|\sum_{a\in A}\sum_{b\in
B}\sum_{c\in C}\sum_{d\in D}\chi(a+b+cd)\right|\] when $A,B,C,D\subset \mathbb
F_p$, the field with $p$ elements and $\chi$ is a non-trivial multiplicative
character modulo $p$.
