We show that the Zhang–Zhang (ZZ) polynomial of a benzenoid obtained by fusing a parallelogram d="mmlsi112" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15003066&_mathId=si112.gif&_user=111111111&_pii=S0166218X15003066&_rdoc=1&_issn=0166218X&md5=925c739ec87b360690caac57072b3e62" title="Click to view the MathML source">M(m,n)dden">de"> with an arbitrary benzenoid structure d="mmlsi130" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15003066&_mathId=si130.gif&_user=111111111&_pii=S0166218X15003066&_rdoc=1&_issn=0166218X&md5=0231ad7c2ddd1ca6487f4b361f23689a" title="Click to view the MathML source">ABCdden">de"> can be simply computed as a product of the ZZ polynomials of both fragments. It seems possible to extend this important result also to cases where both fused structures are arbitrary Kekuléan benzenoids. Formal proofs of explicit forms of the ZZ polynomials for prolate rectangles d="mmlsi14" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15003066&_mathId=si14.gif&_user=111111111&_pii=S0166218X15003066&_rdoc=1&_issn=0166218X&md5=d99165769f919f0e69aaf3a1f88d4a0d" title="Click to view the MathML source">Pr(m,n)dden">de"> and generalized prolate rectangles d="mmlsi15" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15003066&_mathId=si15.gif&_user=111111111&_pii=S0166218X15003066&_rdoc=1&_issn=0166218X&md5=3c524d7167c43565576d8eeafdc57336" title="Click to view the MathML source">Pr([m1,m2,…,mn],n)dden">de"> follow as a straightforward application of the general theory, giving d="mmlsi16" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15003066&_mathId=si16.gif&_user=111111111&_pii=S0166218X15003066&_rdoc=1&_issn=0166218X&md5=3e2d5ee5f21125e164ee68c00aa57868" title="Click to view the MathML source">ZZ(Pr(m,n),x)=(1+(1+x)⋅m)ndden">de"> and d="mmlsi17" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15003066&_mathId=si17.gif&_user=111111111&_pii=S0166218X15003066&_rdoc=1&_issn=0166218X&md5=ac39ff6ac96824e700f5d6914d9c4f8b">dth="383" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0166218X15003066-si17.gif">dden">de">.