College

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 :

Sure! Let's simplify the given expression step-by-step:

The expression we need to simplify is:
[tex]\[ (6x^2 - 3 - 5x^3) - (4x^3 + 2x^2 - 8) \][/tex]

### Step 1: Distribute the negative sign inside the parentheses

When we subtract the second expression, we need to distribute the negative sign to each term inside the parentheses:
[tex]\[ = 6x^2 - 3 - 5x^3 - 4x^3 - 2x^2 + 8 \][/tex]

### Step 2: Combine like terms

Now, we combine the like terms:
- The [tex]\(x^3\)[/tex] terms: [tex]\(-5x^3 - 4x^3 = -9x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(6x^2 - 2x^2 = 4x^2\)[/tex]
- The constant terms: [tex]\(-3 + 8 = 5\)[/tex]

### Step 3: Write the simplified expression

Putting it all together, the simplified expression is:
[tex]\[ -9x^3 + 4x^2 + 5 \][/tex]

So, the final simplified form of the given expression is:
[tex]\[ -9x^3 + 4x^2 + 5 \][/tex]

Among the provided answer choices, this matches:
[tex]\[ -9x^3 + 4x^2 + 5 \][/tex]

Thus, the correct option is:
[tex]\[ \boxed{-9x^3 + 4x^2 + 5} \][/tex]