Let's simplify the given expression step by step.
The original expression you need to simplify is:
[tex]\[
\left(2 x^3 y^2 - 8 x^2 y + 4 y\right) - \left(5 x^3 y^2 - 4 x^2 y - 4 y\right)
\][/tex]
First, distribute the negative sign through the second set of parentheses:
[tex]\[
2 x^3 y^2 - 8 x^2 y + 4 y - 5 x^3 y^2 + 4 x^2 y + 4 y
\][/tex]
Next, combine like terms:
1. For the [tex]\(x^3 y^2\)[/tex] terms:
[tex]\[
2 x^3 y^2 - 5 x^3 y^2 = -3 x^3 y^2
\][/tex]
2. For the [tex]\(x^2 y\)[/tex] terms:
[tex]\[
-8 x^2 y + 4 x^2 y = -4 x^2 y
\][/tex]
3. For the [tex]\(y\)[/tex] terms:
[tex]\[
4 y + 4 y = 8 y
\][/tex]
So, putting it all together, the simplified expression is:
[tex]\[
-3 x^3 y^2 - 4 x^2 y + 8 y
\][/tex]
Thus, the correct simplified expression is:
[tex]\[
-3 x^3 y^2 - 4 x^2 y + 8 y
\][/tex]
Therefore, the correct choice among the given options is:
[tex]\[
\boxed{-3 x^3 y^2 - 4 x^2 y + 8 y}
\][/tex]
