College

Simplify:

[tex]\[

\left(3x^2 - 8x^3 - 7\right) + \left(4x^2 + x^3 - 8\right)

\][/tex]

A. [tex]\(-9x^3 + 7x^2 - 15\)[/tex]

B. [tex]\(-7x^3 + 7x^2 - 15\)[/tex]

C. [tex]\(-9x^3 + 9x^2 - 15\)[/tex]

D. [tex]\(-9x^3 + 9x^2 - 16\)[/tex]

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].