How to induct for double summation?

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I have no idea on how to approach this?

$$ \sum_{i=1}^{n}\sum_{j=1}^{m}a_i + a_j = \sum_{i=1}^{n} a_i + \sum_{i=1}^{m} a_j (it \space may \space be \space wrong \space it \space is \space just \space an \space example) $$

Any hint on induction?

I think the base case is showing n+m = 2

then the induction hypothesis is some thing like this? $$ \sum_{i=1}^{n+1}\sum_{j=1}^{m+1}a_i + a_j = \sum_{i=1}^{n+1} a_i + \sum_{i=1}^{m+1} a_j $$