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]
