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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]
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]
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