EN
For any odd prime p we obtain q-analogues of van Hamme's and Rodriguez-Villegas' supercongruences involving products of three binomial coefficients such as
$∑_{k=0}^{(p-1)/2} [{2k \atop k}]_{q²}^{3} (q^{2k})/((-q²;q²)²_{k}(-q;q)²_{2k}²) ≡ 0 (mod [p]²)$ for p≡ 3 (mod 4),
$∑_{k=0}^{(p-1)/2} [{2k \atop k}]_{q³} ((q;q³)_{k}(q²;q³)_{k}q^{3k})((q⁶;q⁶)_{k}²) ≡ 0 (mod [p]²)$ for p≡ 2 (mod 3),
where $[p] = 1 + q + ⋯ +q^{p-1}$ and $(a;q)ₙ = (1-a)(1-aq)⋯ (1-aq^{n-1})$. We also prove q-analogues of the Sun brothers' generalizations of the above supercongruences. Our proofs are elementary in nature and use the theory of basic hypergeometric series and combinatorial q-binomial identities including a new q-Clausen type summation formula.