Sure, let's simplify the given expression step-by-step.
We start with the expression:
[tex]\[
(4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)
\][/tex]
First, distribute the negative sign through the second parenthesis:
[tex]\[
4n^4 - 8n + 4 - 8n^2 - 4n^4 - 1
\][/tex]
Next, combine like terms. Like terms are the terms that have the same power of [tex]\( n \)[/tex].
Combine the [tex]\( n^4 \)[/tex] terms:
[tex]\[
4n^4 - 4n^4 = 0
\][/tex]
Next, isolate the [tex]\( n^2 \)[/tex] term:
[tex]\[
- 8n^2
\][/tex]
Combine the [tex]\( n \)[/tex] term:
[tex]\[
- 8n
\][/tex]
Finally, combine the constant terms:
[tex]\[
4 - 1 = 3
\][/tex]
Putting it all together, we get the simplified expression:
[tex]\[
-8n^2 - 8n + 3
\][/tex]
So, the simplified form of the expression
[tex]\[
\left(4 n^4-8 n+4\right)-\left(8 n^2+4 n^4+1\right)
\][/tex]
is:
[tex]\[
-8n^2 - 8n + 3
\][/tex]
