I am evaluating some equations where one has products of multiple metrics with $4$-momenta $q$, $p$ and $k$ and getting coordinate sickness slightly. The metric is in fact Minkowski, so we can write it as $\delta_{\mu \nu}$. An example of an expression I have is
$\delta_{\nu \sigma} \delta_{\rho \beta} \delta_{\gamma \mu} \delta^{\mu \nu} \delta^{\beta \gamma} (q-p)^{\rho} (q-p)^{\sigma} = (q-p)_{\beta} (p-r)_{\nu} \delta_{\gamma \mu} \delta^{\mu \nu} \delta^{\beta \gamma},$
which after contracting indices I take to be $16 (q-p) \cdot (p-r)$. Another type of expression is
$\delta_{\nu \sigma} k_{\rho} k_{\beta} \delta_{\gamma \mu} \delta^{\mu \nu} \delta^{\beta \gamma} (q-p)^{\rho} (p-r)^{\sigma}$,
which I take to be equal to $4 k^2 (q-p) \cdot (p-r)$. Is this correct?