Final answer:
To simplify the expression (7n^3 + 3n + 1) - (7n^2 + n + 4), subtract the corresponding terms, resulting in 7n^3 - 7n^2 + 2n - 3 after simplification. The terms are ordered by descending powers of n, which validates the correctness of the answer.
Step-by-step explanation:
To perform the indicated operation and simplify the expression (7n^3 + 3n + 1) - (7n^2 + n + 4), you need to subtract each term in the second parenthesis from the corresponding term in the first parenthesis.
Starting with the highest degree terms:
- 7n^3 is not affected since there is no n^3 term in the second parenthesis.
- Subtract the 7n^2 term: 0n^3 - 7n^2 = -7n^2
- Subtract the n terms from one another: 3n - n = 2n
- Subtract the constant terms: 1 - 4 = -3
Combining all these, the simplified expression becomes: 7n^3 - 7n^2 + 2n - 3.
After simplifying, we check if our answer is reasonable. Each term has been properly subtracted, and the terms are ordered by descending powers of n, which is a standard convention in polynomial expressions.