To simplify the expression \(-4(7b + 3) + 24b - 8\), we can follow these steps:
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Distribute \(-4\) to both terms inside the parentheses: \[ -4(7b) - 4(3) = -28b - 12 \]
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Substitute this back into the expression: \[ -28b - 12 + 24b - 8 \]
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Combine like terms (the \(b\) terms and the constant terms): \[ (-28b + 24b) + (-12 - 8) = -4b - 20 \]
Thus, the simplified expression is: \[ \boxed{-4b - 20} \]