Add or subtract as indicated.

[tex]\[ \left(7n^5 + 2n + 6n^4\right) + \left(9n^4 + 3n^5 + 3n\right) \][/tex]

A. [tex]\(10n^5 + 15n^4 + 5n\)[/tex]
B. [tex]\(30n^{10}\)[/tex]
C. [tex]\(5n^5 + 16n^4 + 9n\)[/tex]
D. [tex]\(10n + 15n^5 + 5n^4\)[/tex]



Answer :

Sure! Let's add the polynomials [tex]\((7n^5 + 2n + 6n^4)\)[/tex] and [tex]\((9n^4 + 3n^5 + 3n)\)[/tex].

First, let's identify and combine the like terms from each polynomial:
1. Combine the [tex]\(n^5\)[/tex] terms:
- From the first polynomial: [tex]\(7n^5\)[/tex]
- From the second polynomial: [tex]\(3n^5\)[/tex]
- Sum: [tex]\(7n^5 + 3n^5 = 10n^5\)[/tex]

2. Combine the [tex]\(n^4\)[/tex] terms:
- From the first polynomial: [tex]\(6n^4\)[/tex]
- From the second polynomial: [tex]\(9n^4\)[/tex]
- Sum: [tex]\(6n^4 + 9n^4 = 15n^4\)[/tex]

3. Combine the [tex]\(n\)[/tex] terms:
- From the first polynomial: [tex]\(2n\)[/tex]
- From the second polynomial: [tex]\(3n\)[/tex]
- Sum: [tex]\(2n + 3n = 5n\)[/tex]

Therefore, the result of adding the two polynomials is:
[tex]\[ 10n^5 + 15n^4 + 5n \][/tex]

So the correct answer is:
[tex]\[ \boxed{10n^5 + 15n^4 + 5n} \][/tex]

Therefore, the correct option is:
A. [tex]\(10n^5 + 15n^4 + 5n\)[/tex]