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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 - 12[/tex]

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

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

Answer :

To find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], let's simplify the given expression step-by-step.

1. Apply the distributive property (also known as the FOIL method):
- First: Multiply the first terms in each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]
- Outer: Multiply the outer terms:
[tex]\[
3x \times -7 = -21x
\][/tex]
- Inner: Multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]
- Last: Multiply the last terms in each binomial:
[tex]\[
-5 \times -7 = 35
\][/tex]

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

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

Therefore, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] simplifies to [tex]\(6x^2 - 31x + 35\)[/tex].

Looking at the options provided, the correct choice is:
- [tex]\(6x^2 - 31x + 35\)[/tex]

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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