To simplify the expression \(-5 + 34(8h + 12) - 10h\), follow these steps:
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Distribute the \(34\) to both terms inside the parentheses: \[ 34(8h) + 34(12) = 272h + 408. \]
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Substitute this back into the expression: \[ -5 + 272h + 408 - 10h. \]
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Combine like terms, starting with the \(h\) terms: \[ 272h - 10h = 262h. \]
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Now combine the constant terms: \[ -5 + 408 = 403. \]
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Putting it all together, we have: \[ 262h + 403. \]
So, the simplified expression is: \[ \boxed{262h + 403}. \]