College

Which expression is equal to [tex]$(3x - 5)(2x - 7)$[/tex]?

A. [tex]$5x^2 - 21x + 12$[/tex]
B. [tex]$6x^2 - 31x - 12$[/tex]
C. [tex]$6x^2 + 31x - 35$[/tex]
D. [tex]$6x^2 - 31x + 35$[/tex]

Answer :

Sure! Let's solve the expression [tex]\((3x - 5)(2x - 7)\)[/tex] step-by-step to find which one of the given options it matches.

### Step-by-Step Solution:

1. Distribute each term in the first bracket to each term in the second bracket:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]

2. Apply the distributive property (FOIL method):
- First: [tex]\(3x \cdot 2x = 6x^2\)[/tex]
- Outer: [tex]\(3x \cdot (-7) = -21x\)[/tex]
- Inner: [tex]\((-5) \cdot 2x = -10x\)[/tex]
- Last: [tex]\((-5) \cdot (-7) = 35\)[/tex]

3. Combine all the terms together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]

4. Combine like terms:
[tex]\[
6x^2 - 31x + 35
\][/tex]

So, the expanded form of [tex]\((3x-5)(2x-7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]

### Conclusion:

The expression [tex]\((3x-5)(2x-7)\)[/tex] matches the option:
[tex]\[
\boxed{6x^2 - 31x + 35}
\][/tex]

Thus, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]