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This paper is concerned with developing some new connection formulae betweentwo generalized classes of Fibonacci and Lucas polynomials. All the connectioncoefficients involve hypergeometric functions of the type $_2F_{1}(z)$, forcertain $z$. Several new connection formulae between some famous polynomialssuch as Fibonacci, Lucas, Pell, Fermat, Pell-Lucas, and Fermat-Lucaspolynomials are deduced as special cases of the derived connection formulae.Some of the introduced formulae generalize some of those existing in theliterature. As two applications of the derived connection formulae, some newformulae linking some celebrated numbers are given and also some newly closedformulae of certain definite weighted integrals are deduced. Based on using thetwo generalized classes of Fibonacci and Lucas polynomials, some new reductionformulae of certain odd and even radicals are developed.

Novel Results of Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals