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Answer :
We start with the expression
$$
9x^2 \left(4x + 2x^2 - 1\right).
$$
**Step 1. Distribute the $9x^2$ to each term inside the parentheses.**
Multiply $9x^2$ by each term:
1. $9x^2 \cdot 4x = 36x^3$
2. $9x^2 \cdot 2x^2 = 18x^4$
3. $9x^2 \cdot (-1) = -9x^2$
**Step 2. Write the resulting expression by combining the terms.**
After the multiplication, we have:
$$
18x^4 + 36x^3 - 9x^2.
$$
Thus, the correct simplification of the expression is
$$
18x^4 + 36x^3 - 9x^2,
$$
which corresponds to option 1.
$$
9x^2 \left(4x + 2x^2 - 1\right).
$$
**Step 1. Distribute the $9x^2$ to each term inside the parentheses.**
Multiply $9x^2$ by each term:
1. $9x^2 \cdot 4x = 36x^3$
2. $9x^2 \cdot 2x^2 = 18x^4$
3. $9x^2 \cdot (-1) = -9x^2$
**Step 2. Write the resulting expression by combining the terms.**
After the multiplication, we have:
$$
18x^4 + 36x^3 - 9x^2.
$$
Thus, the correct simplification of the expression is
$$
18x^4 + 36x^3 - 9x^2,
$$
which corresponds to option 1.
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