Answer :
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.
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.
