To simplify the expression \(3(3y + 9)\), you need to distribute the \(3\) to both terms inside the parentheses.
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Multiply \(3\) by \(3y\): \[ 3 \times 3y = 9y \]
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Multiply \(3\) by \(9\): \[ 3 \times 9 = 27 \]
Now, combine these results: \[ 3(3y + 9) = 9y + 27 \]
Thus, the simplified expression is: \[ \boxed{9y + 27} \]