Question
Add or subtract to simplify
(4n^4-8n+4)-(8n^2+4n^4+1)
(4n^4-8n+4)-(8n^2+4n^4+1)
Answers
GPT-4o mini
To simplify the expression \((4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)\), we will first distribute the negative sign through the second set of parentheses:
\[
(4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1) = 4n^4 - 8n + 4 - 8n^2 - 4n^4 - 1
\]
Next, we will combine like terms. First, let's identify the like terms in the expression:
- The \(n^4\) terms: \(4n^4 - 4n^4 = 0\)
- The \(n^2\ term: -8n^2\)
- The \(n\) terms: \(-8n\)
- The constant terms: \(4 - 1 = 3\)
Now we can combine these results:
\[
0 - 8n^2 - 8n + 3
\]
Thus, the simplified expression is:
\[
-8n^2 - 8n + 3
\]
This is the final simplified form.
\[
(4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1) = 4n^4 - 8n + 4 - 8n^2 - 4n^4 - 1
\]
Next, we will combine like terms. First, let's identify the like terms in the expression:
- The \(n^4\) terms: \(4n^4 - 4n^4 = 0\)
- The \(n^2\ term: -8n^2\)
- The \(n\) terms: \(-8n\)
- The constant terms: \(4 - 1 = 3\)
Now we can combine these results:
\[
0 - 8n^2 - 8n + 3
\]
Thus, the simplified expression is:
\[
-8n^2 - 8n + 3
\]
This is the final simplified form.