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------------------------------------------------ Choose the correct simplification of the expression [tex](7x-3)(4x^2-3x-6)[/tex].

A. [tex]28x^3-33x^2-33x-18[/tex]

B. [tex]28x^3+33x^2-33x+18[/tex]

C. [tex]28x^3-51x^2-33x+18[/tex]

D. [tex]28x^3-33x^2-33x+18[/tex]

To simplify the expression [tex]$(7x - 3)(4x^2 - 3x - 6)$[/tex], we will use the distributive property, also known as the FOIL method for multiplying polynomials. Here's the procedure, broken down step by step:

1. Distribute [tex]$7x$[/tex] across the trinomial [tex]$(4x^2 - 3x - 6)$[/tex]:

- Multiply [tex]$7x$[/tex] by [tex]$4x^2$[/tex]:
[tex]\[
7x \cdot 4x^2 = 28x^3
\][/tex]

- Multiply [tex]$7x$[/tex] by [tex]$-3x$[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]

- Multiply [tex]$7x$[/tex] by [tex]$-6$[/tex]:
[tex]\[
7x \cdot (-6) = -42x
\][/tex]

2. Distribute [tex]$-3$[/tex] across the trinomial [tex]$(4x^2 - 3x - 6)$[/tex]:

- Multiply [tex]$-3$[/tex] by [tex]$4x^2$[/tex]:
[tex]\[
-3 \cdot 4x^2 = -12x^2
\][/tex]

- Multiply [tex]$-3$[/tex] by [tex]$-3x$[/tex]:
[tex]\[
-3 \cdot (-3x) = 9x
\][/tex]

- Multiply [tex]$-3$[/tex] by [tex]$-6$[/tex]:
[tex]\[
-3 \cdot (-6) = 18
\][/tex]

3. Combine all the terms:

- Combine all the terms we obtained from the distribution:
[tex]\[
28x^3 - 21x^2 - 42x - 12x^2 + 9x + 18
\][/tex]

4. Simplify by combining like terms:

- Combine the [tex]$x^2$[/tex] terms:
[tex]\[
-21x^2 - 12x^2 = -33x^2
\][/tex]

- Combine the [tex]$x$[/tex] terms:
[tex]\[
-42x + 9x = -33x
\][/tex]

5. Write the simplified expression:

- Final expression after combining like terms:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]

The simplified form of the expression [tex]$(7x - 3)(4x^2 - 3x - 6)$[/tex] is [tex]$\boxed{28x^3 - 33x^2 - 33x + 18}$[/tex].