Consider the polynomial −4(34p−2n)+6n−(8n+p)

Question

.

Which expression is equivalent to the given polynomial?

(1 point)
Responses

6n−3p
6 n minus 3 p

6n−4p
6 n minus 4 p

−10n−2p
negative 10 n minus 2 p

−10−3p

Answer 1

To simplify the polynomial \(-4(34p - 2n) + 6n - (8n + p)\), let's break it down step by step:

1. Distribute the \(-4\): \[ -4(34p - 2n) = -4 \cdot 34p + -4 \cdot (-2n) = -136p + 8n \]

2. Rewrite the expression: Now we can rewrite the polynomial, replacing the distributed part: \[ -136p + 8n + 6n - (8n + p) \]

3. Distribute the negative sign in the last term: \[ -(8n + p) = -8n - p \]

4. Combine all parts together: Now the full expression is: \[ -136p + 8n + 6n - 8n - p \]

5. Combine like terms:

   • For the \(n\) terms: \[ 8n + 6n - 8n = 6n \]
   • For the \(p\) terms: \[ -136p - p = -137p \]

6. 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.