To find the simplest form of the expression [tex]\((x + 7)(3x - 8)\)[/tex], we need to use the distributive property (also known as the FOIL method for binomials), which stands for First, Outer, Inner, Last:
1. First: Multiply the first terms in each binomial:
[tex]\[
x \cdot 3x = 3x^2
\][/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\[
x \cdot (-8) = -8x
\][/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\[
7 \cdot 3x = 21x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
7 \cdot (-8) = -56
\][/tex]
Next, we add all these products together:
[tex]\[
3x^2 - 8x + 21x - 56
\][/tex]
Combine the like terms [tex]\(-8x\)[/tex] and [tex]\(21x\)[/tex]:
[tex]\[
3x^2 + (21x - 8x) - 56 = 3x^2 + 13x - 56
\][/tex]
Therefore, the simplest form of the expression [tex]\((x + 7)(3x - 8)\)[/tex] is:
[tex]\[
3x^2 + 13x - 56
\][/tex]
So, the answer is:
[tex]\[
\boxed{D. 3x^2 + 13x - 56}
\][/tex]
