To simplify the expression \(-5 + 34(8h + 12) - 10\), follow these steps:
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Distribute the 34 into the parentheses: \[ 34(8h + 12) = 34 \cdot 8h + 34 \cdot 12 = 272h + 408 \]
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Substitute this back into the expression: \[ -5 + 272h + 408 - 10 \]
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Combine the constant terms (-5, 408, and -10): \[ -5 + 408 - 10 = 393 \]
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Now the expression is: \[ 272h + 393 \]
So the simplified expression is: \[ \boxed{272h + 393} \]