To simplify the expression \( 5y - 3(y + 2) \), we follow these steps:
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Distribute the \(-3\) across the terms inside the parentheses: \[ 5y - 3(y + 2) = 5y - 3y - 6 \]
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Combine like terms: \[ 5y - 3y = 2y \]
So, the expression simplifies to: \[ 2y - 6 \]
Therefore, the simplified expression is: \[ \boxed{2y - 6} \]