To simplify the expression [tex]\(6a^4c + 8ac^2 - 4a^4c - 15 - 10ac^2\)[/tex], follow these steps:
1. Identify and group the like terms:
- Combine the terms involving [tex]\(a^4c\)[/tex]: [tex]\(6a^4c\)[/tex] and [tex]\(-4a^4c\)[/tex].
- Combine the terms involving [tex]\(ac^2\)[/tex]: [tex]\(8ac^2\)[/tex] and [tex]\(-10ac^2\)[/tex].
- The constant term is [tex]\(-15\)[/tex], which stands alone.
2. Combine the like terms:
- For the [tex]\(a^4c\)[/tex] terms: [tex]\(6a^4c - 4a^4c = 2a^4c\)[/tex].
- For the [tex]\(ac^2\)[/tex] terms: [tex]\(8ac^2 - 10ac^2 = -2ac^2\)[/tex].
3. Write the simplified expression:
Combining all the simplified parts gives us:
[tex]\[
2a^4c - 2ac^2 - 15
\][/tex]
Therefore, the simplified expression is [tex]\(\boxed{2a^4c - 2ac^2 - 15}\)[/tex].
Thus, the correct answer is:
c. [tex]\(2a^4c - 2ac^2 - 15\)[/tex]
