Multiply: [tex](3x - 2)(2x + 7)[/tex]

A. [tex]5x^2 + 17x + 14[/tex]
B. [tex]6x^2 + 17x - 14[/tex]
C. [tex]6x^2 + 17x + 14[/tex]
D. [tex]6x^2 + 25x - 14[/tex]



Answer :

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].