For each real input, we have a pseduoOut which is commitment to the same amount as the real input. We can therefore subtract the realInputCommitment from the pseudoOut and prove that it is a commitment to zero by signing for it in a ring signature.
Once I do this for each input, how do I then prove that the sum of inputs is equal to the sum of outputs? If I understood correctly, the pseudoOuts are an intermediate step.
Page49 of zero to monero shows a formula whereby: Sum of PseudoOuts = sumOuts + fees * H
This seems to imply that we must choose the blinding factors in the pseduoOuts in such a way that the sum cancels out with the sum of the blinding factors in the real outputs plus fee*H?