To simplify the given expression, [tex]\(2 x^5 + 3 x^3 - 5 x^2 + x^2 + 7 x + 1 + 7 x^8 - 3 x^3 - 4\)[/tex], follow these steps:
1. Identify and group like terms.
Let's write down the given expression and group the terms with the same powers of [tex]\(x\)[/tex]:
[tex]\[
2 x^5 + 3 x^3 - 5 x^2 + x^2 + 7 x + 1 + 7 x^8 - 3 x^3 - 4
\][/tex]
Grouping the terms:
- [tex]\(x^8\)[/tex] terms: [tex]\(7 x^8\)[/tex]
- [tex]\(x^5\)[/tex] terms: [tex]\(2 x^5\)[/tex]
- [tex]\(x^3\)[/tex] terms: [tex]\(3 x^3 - 3 x^3\)[/tex]
- [tex]\(x^2\)[/tex] terms: [tex]\(-5 x^2 + x^2\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(7 x\)[/tex]
- Constant terms: [tex]\(1 - 4\)[/tex]
2. Simplify each group of like terms.
- For the [tex]\(x^8\)[/tex] terms:
[tex]\[
7 x^8
\][/tex]
- For the [tex]\(x^5\)[/tex] terms:
[tex]\[
2 x^5
\][/tex]
- For the [tex]\(x^3\)[/tex] terms:
[tex]\[
3 x^3 - 3 x^3 = 0
\][/tex]
- For the [tex]\(x^2\)[/tex] terms:
[tex]\[
-5 x^2 + x^2 = -4 x^2
\][/tex]
- For the [tex]\(x\)[/tex] terms:
[tex]\[
7 x
\][/tex]
- For the constant terms:
[tex]\[
1 - 4 = -3
\][/tex]
3. Combine all the simplified terms.
Summing them up, we have:
[tex]\[
7 x^8 + 2 x^5 - 4 x^2 + 7 x - 3
\][/tex]
Thus, the simplified expression is:
[tex]\[
7 x^8 + 2 x^5 - 4 x^2 + 7 x - 3
\][/tex]
Now, let's match this with the given choices:
- A. [tex]\(5 x^5+5 x^2+7 x-3\)[/tex]
- B. [tex]\(9 x^5 - 4 x^2 + 7 x + 5\)[/tex]
- C. [tex]\(9 x^5 + 6 x^2 + 7 x + 3\)[/tex]
- D. [tex]\(9 x^5 - 4 x^2 + 7 x - 3\)[/tex]
None of the options directly match our simplified expression. Therefore, the correct answer is not provided in the given choices.
