Answer :
Let's simplify the expression step by step by combining like terms.
The original expression we need to simplify is:
[tex]\[
(3x^2 - 8x^3 - 7) + (4x^2 + x^3 - 8)
\][/tex]
Step 1: Group like terms
1. Terms with [tex]\(x^3\)[/tex]:
- From the first part: [tex]\(-8x^3\)[/tex]
- From the second part: [tex]\(+x^3\)[/tex]
2. Terms with [tex]\(x^2\)[/tex]:
- From the first part: [tex]\(+3x^2\)[/tex]
- From the second part: [tex]\(+4x^2\)[/tex]
3. Constant terms:
- From the first part: [tex]\(-7\)[/tex]
- From the second part: [tex]\(-8\)[/tex]
Step 2: Combine the like terms
1. Combine the [tex]\(x^3\)[/tex] terms:
[tex]\(-8x^3 + x^3 = -7x^3\)[/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\(3x^2 + 4x^2 = 7x^2\)[/tex]
3. Combine the constant terms:
[tex]\(-7 - 8 = -15\)[/tex]
Final Expression:
After combining all like terms, the simplified expression is:
[tex]\[
-7x^3 + 7x^2 - 15
\][/tex]
This matches with one of the given options: [tex]\(-7x^3 + 7x^2 - 15\)[/tex].
The original expression we need to simplify is:
[tex]\[
(3x^2 - 8x^3 - 7) + (4x^2 + x^3 - 8)
\][/tex]
Step 1: Group like terms
1. Terms with [tex]\(x^3\)[/tex]:
- From the first part: [tex]\(-8x^3\)[/tex]
- From the second part: [tex]\(+x^3\)[/tex]
2. Terms with [tex]\(x^2\)[/tex]:
- From the first part: [tex]\(+3x^2\)[/tex]
- From the second part: [tex]\(+4x^2\)[/tex]
3. Constant terms:
- From the first part: [tex]\(-7\)[/tex]
- From the second part: [tex]\(-8\)[/tex]
Step 2: Combine the like terms
1. Combine the [tex]\(x^3\)[/tex] terms:
[tex]\(-8x^3 + x^3 = -7x^3\)[/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\(3x^2 + 4x^2 = 7x^2\)[/tex]
3. Combine the constant terms:
[tex]\(-7 - 8 = -15\)[/tex]
Final Expression:
After combining all like terms, the simplified expression is:
[tex]\[
-7x^3 + 7x^2 - 15
\][/tex]
This matches with one of the given options: [tex]\(-7x^3 + 7x^2 - 15\)[/tex].
