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

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

Answer :

To solve the problem of finding which expression is equal to [tex]\((3x-5)(2x-7)\)[/tex], we can use the distributive property to multiply the two binomials. Here's a step-by-step breakdown:

1. First, multiply the first terms of each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]

2. Next, multiply the outer terms:
[tex]\[
3x \times (-7) = -21x
\][/tex]

3. Then, multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]

4. Finally, multiply the last terms of each binomial:
[tex]\[
-5 \times (-7) = 35
\][/tex]

Now, combine all these results to form the expression:

- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(6x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-21x - 10x = -31x\)[/tex]
- Combine the constant terms: [tex]\(35\)[/tex]

Putting it all together, the expression becomes:
[tex]\[
6x^2 - 31x + 35
\][/tex]

Therefore, the expression equal to [tex]\((3x-5)(2x-7)\)[/tex] is [tex]\(6x^2 - 31x + 35\)[/tex], which corresponds to the first option.

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