To simplify the polynomial \(-4(34p - 2n) + 6n - (8n + p)\), let's break it down step by step:
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Distribute the \(-4\): \[ -4(34p - 2n) = -4 \cdot 34p + -4 \cdot (-2n) = -136p + 8n \]
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Rewrite the expression: Now we can rewrite the polynomial, replacing the distributed part: \[ -136p + 8n + 6n - (8n + p) \]
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Distribute the negative sign in the last term: \[ -(8n + p) = -8n - p \]
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Combine all parts together: Now the full expression is: \[ -136p + 8n + 6n - 8n - p \]
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Combine like terms:
- For the \(n\) terms: \[ 8n + 6n - 8n = 6n \]
- For the \(p\) terms: \[ -136p - p = -137p \]
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Final expression: The simplified expression is: \[ 6n - 137p \]
Now let's compare it to the provided options:
- \(6n - 3p\)
- \(6n - 4p\)
- \(-10n - 2p\)
- \(-10 - 3p\)
None of the provided options matches the simplified expression \(6n - 137p\).
Therefore, it seems there is no equivalent expression provided in your options. Please check if there are any additional choices that might include \(6n - 137p\) or an error in the options.