To simplify the expression \( 3 + 10c + 8(7 + 3c^2) \), we can start by distributing the \( 8 \) across the terms inside the parentheses.
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Distribute \( 8 \): \[ 8(7) + 8(3c^2) = 56 + 24c^2 \]
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Now, substitute this back into the expression: \[ 3 + 10c + 56 + 24c^2 \]
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Combine the constant terms: \[ 3 + 56 = 59 \]
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The simplified expression is: \[ 59 + 10c + 24c^2 \]
Thus, the final simplified expression is: \[ 24c^2 + 10c + 59 \]
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