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

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

Sure, let's work through the problem step-by-step.

We need to multiply the two binomials [tex]$(3x-5)(2x-7)$[/tex]. To do this, we'll use the distributive property (also known as the FOIL method for binomials). The FOIL method stands for First, Outer, Inner, Last, which refers to the terms we need to multiply:

1. First: Multiply the first terms in each binomial:
[tex]\[
(3x) \cdot (2x) = 6x^2
\][/tex]

2. Outer: Multiply the outer terms in the product:
[tex]\[
(3x) \cdot (-7) = -21x
\][/tex]

3. Inner: Multiply the inner terms in the product:
[tex]\[
(-5) \cdot (2x) = -10x
\][/tex]

4. Last: Multiply the last terms in each binomial:
[tex]\[
(-5) \cdot (-7) = 35
\][/tex]

Now, we add all these results together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]

Combine the like terms [tex]$-21x$[/tex] and [tex]$-10x$[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]

So, the expression [tex]$(3x-5)(2x-7)$[/tex] expands to:
[tex]\[
6x^2 - 31x + 35
\][/tex]

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

The expression corresponding to this result is:
[tex]\[
6x^2 - 31x + 35
\][/tex]

Thus, the correct choice from the given options is:
[tex]\[
6x^2 - 31x + 35
\][/tex]