Select the correct answer.

What is the standard form of this expression?

[tex]\[
(3x + 4)(x - 8)
\][/tex]

A. [tex]\(3x^2 - 4x - 32\)[/tex]

B. [tex]\(3x^2 - 20x - 32\)[/tex]

C. [tex]\(3x^2 - 4x - 12\)[/tex]

D. [tex]\(3x^2 - 20x - 12\)[/tex]



Answer :

To express [tex]\((3x + 4)(x - 8)\)[/tex] in standard form, we need to multiply the two binomials together and then combine like terms. The standard form of a quadratic expression is [tex]\(Ax^2 + Bx + C\)[/tex].

1. Distribute [tex]\(3x + 4\)[/tex] over [tex]\(x - 8\)[/tex]:

[tex]\[ (3x + 4)(x - 8) = (3x)(x) + (3x)(-8) + (4)(x) + (4)(-8) \][/tex]

2. Perform the multiplications:

[tex]\[ (3x)(x) = 3x^2 \][/tex]
[tex]\[ (3x)(-8) = -24x \][/tex]
[tex]\[ (4)(x) = 4x \][/tex]
[tex]\[ (4)(-8) = -32 \][/tex]

3. Combine the resulting terms:

[tex]\[ 3x^2 - 24x + 4x - 32 \][/tex]

4. Combine the like terms [tex]\(-24x\)[/tex] and [tex]\(4x\)[/tex]:

[tex]\[ 3x^2 - 20x - 32 \][/tex]

Therefore, the correct standard form of [tex]\((3x + 4)(x - 8)\)[/tex] is:

[tex]\[ 3x^2 - 20x - 32 \][/tex]

Thus, the correct answer is:

[tex]\[ \boxed{3x^2 - 20x - 32} \][/tex]