Answer :
Let's add the two polynomials step-by-step:
We start with the expression:
[tex]\[
(7x^6 + 10x^2 - 10) + (3x^6 - 6x^3 + 4)
\][/tex]
1. Combine like terms. We'll add the coefficients of terms with the same degree:
- [tex]\(x^6\)[/tex] terms: [tex]\(7x^6 + 3x^6 = 10x^6\)[/tex]
- [tex]\(x^3\)[/tex] terms: There is no [tex]\(x^3\)[/tex] term in the first polynomial, so we only have [tex]\(-6x^3\)[/tex].
- [tex]\(x^2\)[/tex] terms: [tex]\(10x^2\)[/tex] is the only [tex]\(x^2\)[/tex] term present.
- Constant terms: [tex]\(-10 + 4 = -6\)[/tex]
2. Write the complete expression:
[tex]\[
10x^6 - 6x^3 + 10x^2 - 6
\][/tex]
This gives us the final result: [tex]\(10x^6 - 6x^3 + 10x^2 - 6\)[/tex].
So, the correct choice is [tex]\( \boxed{10x^6 - 6x^3 + 10x^2 - 6} \)[/tex].
We start with the expression:
[tex]\[
(7x^6 + 10x^2 - 10) + (3x^6 - 6x^3 + 4)
\][/tex]
1. Combine like terms. We'll add the coefficients of terms with the same degree:
- [tex]\(x^6\)[/tex] terms: [tex]\(7x^6 + 3x^6 = 10x^6\)[/tex]
- [tex]\(x^3\)[/tex] terms: There is no [tex]\(x^3\)[/tex] term in the first polynomial, so we only have [tex]\(-6x^3\)[/tex].
- [tex]\(x^2\)[/tex] terms: [tex]\(10x^2\)[/tex] is the only [tex]\(x^2\)[/tex] term present.
- Constant terms: [tex]\(-10 + 4 = -6\)[/tex]
2. Write the complete expression:
[tex]\[
10x^6 - 6x^3 + 10x^2 - 6
\][/tex]
This gives us the final result: [tex]\(10x^6 - 6x^3 + 10x^2 - 6\)[/tex].
So, the correct choice is [tex]\( \boxed{10x^6 - 6x^3 + 10x^2 - 6} \)[/tex].
