To simplify the expression \(310x + 16y + 310x + 36y\), we can combine like terms.
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Combine the \(x\) terms: \[ 310x + 310x = 620x \]
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Combine the \(y\) terms: \[ 16y + 36y = 52y \]
Now, we put the combined terms together: \[ 620x + 52y \]
Thus, the simplified expression is: \[ \boxed{620x + 52y} \]