We show that the Zhang–Zhang (ZZ) polynomial of a benzenoid obtained by fusing a parallelogram lsi112" class="mathmlsrc">lass="formulatext stixSupport mathImg" 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)lass="mathContainer hidden">lass="mathCode"> with an arbitrary benzenoid structure lsi130" class="mathmlsrc">lass="formulatext stixSupport mathImg" 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">ABClass="mathContainer hidden">lass="mathCode"> 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 lsi14" class="mathmlsrc">lass="formulatext stixSupport mathImg" 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)lass="mathContainer hidden">lass="mathCode"> and generalized prolate rectangles lsi15" class="mathmlsrc">lass="formulatext stixSupport mathImg" 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)lass="mathContainer hidden">lass="mathCode"> follow as a straightforward application of the general theory, giving lsi16" class="mathmlsrc">lass="formulatext stixSupport mathImg" 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)nlass="mathContainer hidden">lass="mathCode"> and lsi17" class="mathmlsrc">le="View the MathML source" class="mathImg" 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">lass="imgLazyJSB inlineImage" height="19" width="383" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0166218X15003066-si17.gif">lass="mathContainer hidden">lass="mathCode">.