Answer :

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!