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]



Answer :

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]