Question

Consider the polynomial expression -4 (3/4p - 2n) + 6n - (8n + p)
Which expression is equivalent to the given polynomial?
1. 6n - 3p
2. 6n - 4p
3. -10n - 2p
4. -10n - 3p

Answer 1

To simplify the expression \(-4(3/4p - 2n) + 6n - (8n + p)\), we will start by distributing and combining like terms step by step.

First, distribute \(-4\) in the first term:

\[
-4(3/4p) + -4(-2n) = -3p + 8n
\]

Now we can rewrite the entire expression as:

\[
-3p + 8n + 6n - (8n + p)
\]

Next, distribute the negative sign in the last term:

\[
-3p + 8n + 6n - 8n - p
\]

Now combine like terms:

Combining the \(n\) terms:

\[
8n + 6n - 8n = 6n
\]

Combining the \(p\) terms:

\[
-3p - p = -4p
\]

Putting it all together, we get the simplified expression:

\[
6n - 4p
\]

Thus, the expression equivalent to the given polynomial is:

\(\boxed{2. \, 6n - 4p}\)