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.

Explore how to solve the function composition problem (f•g)(x)=(-4x²+2x²)(x+3). This solution breaks down key algebraic concepts like polynomial simplification and function composition, suitable for students in Grades 9-11.

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