We study certain polynomials
![$ P_{m}\left( x,y;t\right) $](img2.gif)
and
![$ Q_{m}\left(
x,y;t\right) $](img3.gif)
of the variable
![$ t$](img4.gif)
whose coefficients involve bivariate
Fibonacci polynomials
![$ F_{j}\left( x,y\right) $](img5.gif)
or bivariate Lucas
polynomials
![$ L_{j}\left( x,y\right) $](img6.gif)
. By working with
![$ P_{m}\left(
x,y;tx\right) $](img7.gif)
and
![$ Q_{m}\left( x,y;tx\right) $](img8.gif)
, together with the
generating functions for Bernoulli polynomials
![$ B_{i}\left( t\right) $](img9.gif)
and
Euler polynomials
![$ E_{i}\left( t\right) $](img10.gif)
, we obtain a list of eight
identities connecting
![$ F_{j}\left( x,y\right) $](img5.gif)
or
![$ L_{j}\left( x,y\right) $](img6.gif)
with
![$ B_{i}\left( t\right) $](img9.gif)
or
![$ E_{i}\left( t\right) $](img10.gif)
. We present also
some consequences of these results.