We study sums of powers of Fibonacci and Lucas polynomials of the form $%\sum_{n=0}^{q}F_{tsn}^{k}(x) $ and $\sum_{n=0}^{q}L_{tsn}^{k}% (x) $, where$s,t,k$ are given natural numbers, together with the corresponding alternatingsums $\sum_{n=0}^{q}(-1) ^{n}F_{tsn}^{k}(x) $ and $\sum_{n=0}^{q}(-1)^{n}L_{tsn}^{k}(x) $. We give sufficient conditions on the parameters $s,t,k$for express these sums as linear combinations of certain $s$-Fibopolynomials.
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