Sure, let's simplify the given expression step by step:
Given expression:
[tex]\[ 2\left(3 x^2 + 2 x^3 - 9 - 4 x^2 - 5 x + 1 - 3 x^3 + x^2\right) \][/tex]
First, we need to combine like terms inside the parentheses. To do this, we group the terms with the same powers of [tex]\( x \)[/tex]:
[tex]\[
3 x^2 - 4 x^2 + x^2 + 2 x^3 - 3 x^3 - 5 x - 9 + 1
\][/tex]
Now, combine the coefficients of like terms:
1. For [tex]\( x^2 \)[/tex]:
[tex]\[ 3 x^2 - 4 x^2 + x^2 = (3 - 4 + 1)x^2 = 0 x^2 = 0 \][/tex]
2. For [tex]\( x^3 \)[/tex]:
[tex]\[ 2 x^3 - 3 x^3 = (2 - 3)x^3 = -x^3 \][/tex]
3. For the constants:
[tex]\[ -9 + 1 = -8 \][/tex]
4. For [tex]\( x \)[/tex]:
[tex]\[ -5x \][/tex] (there is only one [tex]\( x \)[/tex] term)
Putting these terms together within the parentheses, we get:
[tex]\[
0 + (-x^3) - 8 - 5x
\][/tex]
which simplifies to:
[tex]\[
- x^3 - 8 - 5x
\][/tex]
Next, we multiply this simplified expression by 2:
[tex]\[
2(- x^3 - 8 - 5x)
\][/tex]
Distributing 2 across each term inside the parentheses, we get:
[tex]\[
2(- x^3) + 2(- 8) + 2(- 5x)
\][/tex]
This further simplifies to:
[tex]\[
- 2x^3 - 16 - 10x
\][/tex]
So, the simplified form of the given expression is:
[tex]\[
- 2x^3 - 16 - 10x
\][/tex]
And that is the solution!
