Simplify the following expression:

[tex]\[ 6a^4c + 8ac^2 - 4a^4c - 15 - 10ac^2 \][/tex]

A. [tex]\[ 2a^4c - 2ac^2 \][/tex]

B. [tex]\[ -4a^4c + 4ac^2 - 30 \][/tex]

C. [tex]\[ 2a^4c - 2ac^2 - 15 \][/tex]

D. [tex]\[ 2a^4c + 17ac^2 - 15 \][/tex]



Answer :

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]