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

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

To find which expression is equal to [tex]$(3x-5)(2x-7)$[/tex], let's multiply these two binomials using the distributive property, also known as the FOIL method (First, Outer, Inner, Last).

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

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

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

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

Now, combine all these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]

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

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

Therefore, the correct choice is: [tex]$6x^2 - 31x + 35$[/tex].