How can we calculate the tensor product of Lagrange basis polynomials?

Question

Given data points $(x_i,y_i)$, the Lagrange basis polynomials are $$\mathcal l_j(x):=\sum_{i\ne j}\frac{x-x_i}{x_j-x_i}\;.$$ I'm reading a text targeting Smolyak's algorithm. In this text, they use tensor products $$\mathcal l_{j_1}\otimes\mathcal l_{j_2}\otimes\mathcal l_{j_3}\cdots$$ of these basis polynomials. I need to explicitly calculate these tensor products. So, what exactly is $\mathcal l_{j_1}\otimes\mathcal l_{j_2}$?