  In this work, some of the NLO QCD corrections for pp -> VVjj + X are
presented. A program in Mathematica based on the structure of FeynCalc which
automatically simplifies a set of amplitudes up to the hexagon level of rank 5
has been created for this purpose. We focus on two different topologies. The
first involves all the virtual contributions needed for quadruple electroweak
vector boson production, i.e. pp -> VVVV + X. In the second, the remaining
"bosonic" corrections to electroweak triple vector boson production with an
additional jet (pp -> VVV j + X) are computed. We show the factorization
formula of the infrared divergences of the bosonic contributions for VVVV and
VVVj production with V=(W,Z,gamma). Stability issues associated with the
evaluation of the hexagons up to rank 5 are studied. The CPU time of the
FORTRAN subroutines rounds the 2 milliseconds and seems to be competitive with
other more sophisticated methods. Additionally, in Appendix A the master
equations to obtain the tensor coefficients up to the hexagon level in the
external momenta convention are presented including the ones needed for small
Gram determinants.
