Question

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

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.