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Simplify [tex]\left(6x^2 - 3 - 5x^3\right) - \left(4x^3 + 2x^2 - 8\right)[/tex].

A. [tex]9x^3 - 4x^2 - 5[/tex]
B. [tex]-9x^3 + 4x^2 + 5[/tex]
C. [tex]x^3 - x^2 - 13x^3[/tex]
D. [tex]-x^3 + x^2 + 13x^3[/tex]

Answer :

Let's simplify the expression [tex]\((6x^2 - 3 - 5x^3) - (4x^3 + 2x^2 - 8)\)[/tex] step by step.

### Step 1: Distribute the Negative Sign
We need to distribute the negative sign to each term in the second polynomial:

[tex]\[
(6x^2 - 3 - 5x^3) - 4x^3 - 2x^2 + 8
\][/tex]

### Step 2: Rearrange and Combine Like Terms
Now, let's rearrange the terms and combine like terms:

- Terms with [tex]\(x^3\)[/tex]: [tex]\(-5x^3 - 4x^3 = -9x^3\)[/tex]
- Terms with [tex]\(x^2\)[/tex]: [tex]\(6x^2 - 2x^2 = 4x^2\)[/tex]
- Constant terms: [tex]\(-3 + 8 = 5\)[/tex]

### Step 3: Write the Simplified Expression
Combining all the simplified parts, we get:

[tex]\[
-9x^3 + 4x^2 + 5
\][/tex]

Therefore, the correct answer is: [tex]\(-9x^3 + 4x^2 + 5\)[/tex].

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