To simplify the expression \( 6(13 - 3^2) + 1 \), follow these steps:
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Calculate \( 3^2 \): \[ 3^2 = 9 \]
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Substitute \( 9 \) back into the expression: \[ 6(13 - 9) + 1 \]
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Now simplify inside the parentheses: \[ 13 - 9 = 4 \]
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Substitute \( 4 \) back into the expression: \[ 6(4) + 1 \]
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Next, multiply \( 6 \) by \( 4 \): \[ 6 \times 4 = 24 \]
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Finally, add \( 1 \): \[ 24 + 1 = 25 \]
Thus, the simplified expression is: \[ \boxed{25} \]