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------------------------------------------------ Choose the correct simplification of [tex]9x^2(4x + 2x^2 - 1)[/tex].

A. [tex]18x^4 + 36x^3 - 9x^2[/tex]

B. [tex]18x^4 - 35x^3 + 9x^2[/tex]

C. [tex]36x^4 + 18x^3 - 9x^2[/tex]

D. [tex]36x^4 - 13x^3 + 9x^2[/tex]

To simplify the expression [tex]$ 9x^2(4x + 2x^2 - 1) $[/tex], we need to distribute [tex]$ 9x^2 $[/tex] to each term inside the parentheses. Here’s how this can be done step-by-step:

1. Distribute [tex]$ 9x^2 $[/tex]:

- Multiply [tex]$ 9x^2 $[/tex] with [tex]$ 4x $[/tex]:
[tex]\[
9x^2 \times 4x = 36x^3
\][/tex]

- Multiply [tex]$ 9x^2 $[/tex] with [tex]$ 2x^2 $[/tex]:
[tex]\[
9x^2 \times 2x^2 = 18x^4
\][/tex]

- Multiply [tex]$ 9x^2 $[/tex] with [tex]$-1$[/tex]:
[tex]\[
9x^2 \times -1 = -9x^2
\][/tex]

2. Combine these results:

Now, combine all the results from the distribution:
[tex]\[
18x^4 + 36x^3 - 9x^2
\][/tex]

Thus, the simplified form of the expression [tex]$ 9x^2(4x + 2x^2 - 1) $[/tex] is:

[tex]\[ 18x^4 + 36x^3 - 9x^2 \][/tex]

Comparing this with the provided choices, the correct option is:

a) [tex]$ 18x^4 + 36x^3 - 9x^2 $[/tex]