Answer :
Sure! Let's solve the algebraic subtraction step by step.
You have two polynomials:
1. [tex]\(8x^9 + 6x^7 - 7x^3 + 2\)[/tex]
2. [tex]\(2x^9 - 7x^5 + 6x^3 - 9\)[/tex]
We want to subtract the second polynomial from the first:
[tex]\[
(8x^9 + 6x^7 - 7x^3 + 2) - (2x^9 - 7x^5 + 6x^3 - 9)
\][/tex]
To do this, distribute the negative sign through the second polynomial:
[tex]\[
8x^9 + 6x^7 - 7x^3 + 2 - 2x^9 + 7x^5 - 6x^3 + 9
\][/tex]
Next, let's combine like terms:
- [tex]\(x^9\)[/tex] terms: [tex]\(8x^9 - 2x^9 = 6x^9\)[/tex]
- [tex]\(x^7\)[/tex] terms: There is only [tex]\(6x^7\)[/tex].
- [tex]\(x^5\)[/tex] terms: There is only [tex]\(+7x^5\)[/tex].
- [tex]\(x^3\)[/tex] terms: [tex]\(-7x^3 - 6x^3 = -13x^3\)[/tex]
- Constant terms: [tex]\(2 + 9 = 11\)[/tex]
Putting it all together, the simplified polynomial is:
[tex]\[
6x^9 + 6x^7 + 7x^5 - 13x^3 + 11
\][/tex]
Therefore, the correct response is:
[tex]\[
6x^9 + 6x^7 + 7x^5 - 13x^3 + 11
\][/tex]
You have two polynomials:
1. [tex]\(8x^9 + 6x^7 - 7x^3 + 2\)[/tex]
2. [tex]\(2x^9 - 7x^5 + 6x^3 - 9\)[/tex]
We want to subtract the second polynomial from the first:
[tex]\[
(8x^9 + 6x^7 - 7x^3 + 2) - (2x^9 - 7x^5 + 6x^3 - 9)
\][/tex]
To do this, distribute the negative sign through the second polynomial:
[tex]\[
8x^9 + 6x^7 - 7x^3 + 2 - 2x^9 + 7x^5 - 6x^3 + 9
\][/tex]
Next, let's combine like terms:
- [tex]\(x^9\)[/tex] terms: [tex]\(8x^9 - 2x^9 = 6x^9\)[/tex]
- [tex]\(x^7\)[/tex] terms: There is only [tex]\(6x^7\)[/tex].
- [tex]\(x^5\)[/tex] terms: There is only [tex]\(+7x^5\)[/tex].
- [tex]\(x^3\)[/tex] terms: [tex]\(-7x^3 - 6x^3 = -13x^3\)[/tex]
- Constant terms: [tex]\(2 + 9 = 11\)[/tex]
Putting it all together, the simplified polynomial is:
[tex]\[
6x^9 + 6x^7 + 7x^5 - 13x^3 + 11
\][/tex]
Therefore, the correct response is:
[tex]\[
6x^9 + 6x^7 + 7x^5 - 13x^3 + 11
\][/tex]
