Pell and Pell-Lucas polynomials are given recursively by \(P_n(x)=2xP_{n-1}(x)+P_{n-2}(x)\) and \(Q_n(x)=2xQ_{n-1}(x)+Q_{n-2}(x)\), respectively, with initial conditions \(P_0(x)=0, P_1(x)=1, Q_0(x)=2, Q_1(x)=2x\). They generalize the Fibonacci and Lucas numbers, which correspond to \(F_n=P_n(\frac 12)\) and \(L_n=Q_n(\frac 12)\), respectively. The authors establish a set of identities for some weighted binomial sums of the form \(\sum_{k=0}^n (\pm 1)^k \binom{2n+\delta}{n-k} W_k(x)\), where \(W_k(x)=P_{2k+\varepsilon}(x), Q_{2k+\varepsilon}(x), P_k^2(x)\), and \(Q_k^2(x)\), with \(\delta, \varepsilon\in\{0,1\}\). As an example, from Theorem 1, \[ \sum_{k=0}^n\binom {2n+\delta}{n-k} P_{2k+1}= (4+4x^2)^n+ (\delta -1) \sum_{i=1}^n \binom {2i}{i} \frac{(4+4x^2)^{n-i}}{2(2i-1)}. \] By letting \(x=\frac 12\) in each result, we can verify the particular identities involving Fibonacci and Lucas numbers, two of which (Equations 1 and 2) have appeared in a recent challenge problem.