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

Answer :

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

1. Distribute each term in the first binomial [tex]\((3x - 5)\)[/tex] by each term in the second binomial [tex]\((2x - 7)\)[/tex]:

[tex]\[
(3x - 5)(2x - 7)
\][/tex]

2. Multiply [tex]\(3x\)[/tex] by each term in the second binomial:

[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot -7 = -21x
\][/tex]

3. Now, multiply [tex]\(-5\)[/tex] by each term in the second binomial:

[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot -7 = 35
\][/tex]

4. Add together all the resulting terms:

[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]

5. Combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:

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

So, the expanded form of the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is:

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

Therefore, the expression equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:

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

Hence, the correct option is:

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

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