Let's simplify the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex] step-by-step.
First, we'll distribute each term in [tex]\((7x - 3)\)[/tex] to each term in [tex]\((4x^2 - 3x - 6)\)[/tex].
1. Distributing [tex]\(7x\)[/tex]:
[tex]\[ 7x \cdot 4x^2 = 28x^3 \][/tex]
[tex]\[ 7x \cdot -3x = -21x^2 \][/tex]
[tex]\[ 7x \cdot -6 = -42x \][/tex]
2. Distributing [tex]\(-3\)[/tex]:
[tex]\[ -3 \cdot 4x^2 = -12x^2 \][/tex]
[tex]\[ -3 \cdot -3x = 9x \][/tex]
[tex]\[ -3 \cdot -6 = 18 \][/tex]
Now, we combine the results from both distributions:
[tex]\[ 28x^3 + (-21x^2) + (-42x) + (-12x^2) + 9x + 18 \][/tex]
Next, we combine like terms:
1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ -21x^2 + (-12x^2) = -33x^2 \][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -42x + 9x = -33x \][/tex]
So, the simplified expression is:
[tex]\[ 28x^3 - 33x^2 - 33x + 18 \][/tex]
Among the given options, the correct simplification of the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex] is:
[tex]\[ \boxed{28x^3 - 33x^2 - 33x + 18} \][/tex]
