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 (First, Outer, Inner, Last). Let's expand it step by step:
1. First: Multiply the first terms in each binomial.
- [tex]\(x \cdot 3x = 3x^2\)[/tex]
2. Outer: Multiply the outer terms in the binomials.
- [tex]\(x \cdot -8 = -8x\)[/tex]
3. Inner: Multiply the inner terms in the binomials.
- [tex]\(7 \cdot 3x = 21x\)[/tex]
4. Last: Multiply the last terms in each binomial.
- [tex]\(7 \cdot -8 = -56\)[/tex]
Next, combine these results:
[tex]\[
3x^2 - 8x + 21x - 56
\][/tex]
Now, combine the like terms ([tex]\(-8x + 21x\)[/tex]):
[tex]\[
3x^2 + 13x - 56
\][/tex]
Therefore, the simplest form of the expression [tex]\((x + 7)(3x - 8)\)[/tex] is:
[tex]\[
3x^2 + 13x - 56
\][/tex]
Hence, the correct answer is:
D. [tex]\(3x^2 + 13x - 56\)[/tex]
