Sure, let's multiply the given binomials step-by-step to arrive at the correct answer.
Given: [tex]\((3x - 2)(2x + 7)\)[/tex]
### Step-by-Step Solution
We will use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to expand the product of the binomials.
1. First Terms:
Multiply the first terms in each binomial:
[tex]\[
(3x) \cdot (2x) = 6x^2
\][/tex]
2. Outer Terms:
Multiply the outer terms in the product:
[tex]\[
(3x) \cdot (7) = 21x
\][/tex]
3. Inner Terms:
Multiply the inner terms in the product:
[tex]\[
(-2) \cdot (2x) = -4x
\][/tex]
4. Last Terms:
Multiply the last terms in each binomial:
[tex]\[
(-2) \cdot (7) = -14
\][/tex]
### Combining Like Terms
Now, let's combine the like terms (the `x` terms):
[tex]\[
21x - 4x = 17x
\][/tex]
### Final Result
Combine all the terms to get the expanded form of the product:
[tex]\[
6x^2 + 17x - 14
\][/tex]
Therefore, the correct answer is:
[tex]\[
6x^2 + 17x - 14
\][/tex]
Among the given options:
- [tex]\(6x^2 + 17x - 14\)[/tex] is the correct one.
### Conclusion
The expanded form of [tex]\((3x - 2)(2x + 7)\)[/tex] is [tex]\(6x^2 + 17x - 14\)[/tex].
