We study the previously introduced bracketed tiling construction and obtain direct proofs of some identities for the Fibonacci and Lucas numbers. By adding a new type of tile we call a superdomino to this construction, we obtain combinatorial proofs of some formulas for the Fibonacci and Lucas polynomials, which we were unable to find in the literature. Special cases of these formulas occur in the text by Benjamin and Quinn, where the question of finding their combinatorial proofs is raised. In the process, we also show, via direct bijections, that the bracketed (2n)-bracelets as well as the linear bracketed (2n + 1)-tilings both number 5n.
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