Polymer random walk question

I understand the mean square end-to-end distance of a polymer of stepsize b and number of units N is given by

$$\left\langle R^{2}\right\rangle = \sum_{i,j=1}^{N} \left\langle r_{i} r_{j}\right\rangle + \left\langle \sum_{i \neq j}^{N} r_{i} r_{j}\right\rangle$$

And that the cross terms drop out to produce the solution of Nb^2. However I don't understand the origin of these cross terms in the first place - what do they physically represent? And how would one evaluate the sum in the cross terms??