Answer :
Let's simplify the expression [tex]\((3x^2 - 3 + 9x^3) - (4x^3 - 2x^2 + 16)\)[/tex].
### Step 1: Distribute the Negative Sign
First, distribute the negative sign across the terms inside the second set of parentheses:
[tex]\[
-(4x^3 - 2x^2 + 16) = -4x^3 + 2x^2 - 16
\][/tex]
### Step 2: Rewrite the Expression
Now, rewrite the original expression with the terms we just distributed:
[tex]\[
(3x^2 - 3 + 9x^3) - (4x^3 - 2x^2 + 16) = 3x^2 - 3 + 9x^3 - 4x^3 + 2x^2 - 16
\][/tex]
### Step 3: Combine Like Terms
Next, combine the like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
9x^3 - 4x^3 = 5x^3
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
3x^2 + 2x^2 = 5x^2
\][/tex]
- Combine the constant terms:
[tex]\[
-3 - 16 = -19
\][/tex]
### Step 4: Write the Simplified Expression
Put it all together to get the simplified expression:
[tex]\[
5x^3 + 5x^2 - 19
\][/tex]
This is the simplified version of the given expression.
### Step 1: Distribute the Negative Sign
First, distribute the negative sign across the terms inside the second set of parentheses:
[tex]\[
-(4x^3 - 2x^2 + 16) = -4x^3 + 2x^2 - 16
\][/tex]
### Step 2: Rewrite the Expression
Now, rewrite the original expression with the terms we just distributed:
[tex]\[
(3x^2 - 3 + 9x^3) - (4x^3 - 2x^2 + 16) = 3x^2 - 3 + 9x^3 - 4x^3 + 2x^2 - 16
\][/tex]
### Step 3: Combine Like Terms
Next, combine the like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
9x^3 - 4x^3 = 5x^3
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
3x^2 + 2x^2 = 5x^2
\][/tex]
- Combine the constant terms:
[tex]\[
-3 - 16 = -19
\][/tex]
### Step 4: Write the Simplified Expression
Put it all together to get the simplified expression:
[tex]\[
5x^3 + 5x^2 - 19
\][/tex]
This is the simplified version of the given expression.
