To do a favor for someone expecting a favor in return.
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To do someone a favor because you expect one back.
Scratch my back and I'll scratch yours means both sides help each other.
It can be friendly, or it can sound like a deal made behind closed doors.
"Quid Pro Quo"
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A formal or explicit exchange where something is given only in return for something else
"Mutual Back-scratching"
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The same concept as scratch each other's backs — an arrangement where favors go both ways
"Scratch Someone's Back"
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Doing a favor for someone without expecting anything in return