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