Let's simplify the expression $(f \circ g)(x)$, which is defined as $(f \circ g)(x) = f(g(x))$. The given expression is:

$(f \circ g)(x) = (-4x^2 + 2x^2)(x + 3)$

Step 1: Simplify the terms inside the parentheses.

The expression inside the first parentheses is $-4x^2 + 2x^2$, which can be simplified:

$-4x^2 + 2x^2 = -2x^2$

Step 2: Multiply by $(x + 3)$.

Now we multiply $-2x^2$ by $(x + 3)$:

$-2x^2(x + 3) = -2x^2 \cdot x - 2x^2 \cdot 3$

This simplifies to:

$-2x^3 - 6x^2$

Final Answer:

$(f \circ g)(x) = -2x^3 - 6x^2$

Would you like more details on any step?

Here are some related questions:

1. What is the difference between function composition and multiplication?
2. How do you interpret the notation $f(g(x))$ in general terms?
3. How would you find the domain of the composed function $f \circ g$?
4. Can you decompose a more complex function using similar steps?
5. What are common errors when simplifying polynomial expressions?

Tip: Always simplify expressions inside parentheses before applying any multiplication or composition steps.