College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which expression is equal to [tex]$(3x - 5)(2x - 7)$[/tex]?

A. [tex]$6x^2 - 31x - 12$[/tex]

B. [tex]$5x^2 - 21x + 12$[/tex]

C. [tex]$6x^2 - 31x + 35$[/tex]

D. [tex]$6x^2 + 31x - 35$[/tex]

Answer :

To determine which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we can expand the given product:

1. Distribute each term in the first binomial to each term in the second binomial:
- First, distribute [tex]\(3x\)[/tex] to both terms in [tex]\(2x - 7\)[/tex]:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot (-7) = -21x
\][/tex]

- Next, distribute [tex]\(-5\)[/tex] to both terms in [tex]\(2x - 7\)[/tex]:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot (-7) = 35
\][/tex]

2. Combine all of these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]

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

So, the expanded expression is [tex]\(6x^2 - 31x + 35\)[/tex].

Let's match this expression with the given options:

1. [tex]\(6x^2 - 31x - 12\)[/tex]
2. [tex]\(5x^2 - 21x + 12\)[/tex]
3. [tex]\(6x^2 - 31x + 35\)[/tex]
4. [tex]\(6x^2 + 31x - 35\)[/tex]

The expression [tex]\(6x^2 - 31x + 35\)[/tex] matches exactly with the third option.

Therefore, the expression that is equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[ \boxed{6x^2 - 31x + 35} \][/tex]