Final answer:
The subtraction of the second polynomial from the first and combining like terms results in the simplified expression 2j^3 - j^12 - 7. However, this expression does not match any of the presented answer choices.
Step-by-step explanation:
To simplify the expression (8j^3 - 10j^2 - 7) - (6j^3 - 10j^2 - j^12), we need to subtract the second polynomial from the first. This involves combining like terms, which are terms with the same variable raised to the same power. We do this by subtracting the coefficients of like terms.
The like terms here are those with j^3 and j^2. There are no other like terms with j^12 or the constant term -7, so these remain unchanged in the expression after subtraction.
First, for the j^3 terms:
8j^3 - 6j^3 = 2j^3
Second, for the j^2 terms:
-10j^2 - (-10j^2) = -10j^2 + 10j^2 = 0
As there is no j^12 term in the first polynomial and a -j^12 term in the second, after subtraction, we have -j^12.
Finally, the constant terms: -7 from the first polynomial remains as there is no corresponding constant in the second.
Therefore, the simplified expression is 2j^3 - j^12 - 7. However, as this does not match any of the options given in the question, it seems there may be some error in the question or the answer choices provided.