Answer :
To find the expression that is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we need to expand the given product [tex]\((3x - 5)(2x - 7)\)[/tex].
Let's break it down step-by-step:
1. Expand the binomials:
[tex]\[
(3x - 5)(2x - 7) = 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
2. Multiply the terms:
[tex]\[
= 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
[tex]\[
= 6x^2 + (-21x) + (-10x) + 35
\][/tex]
3. Combine the like terms (the [tex]\(x\)[/tex] terms):
[tex]\[
= 6x^2 - 21x - 10x + 35
\][/tex]
[tex]\[
= 6x^2 - 31x + 35
\][/tex]
So the expression that matches the expanded product of [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct answer is:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
Let's break it down step-by-step:
1. Expand the binomials:
[tex]\[
(3x - 5)(2x - 7) = 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
2. Multiply the terms:
[tex]\[
= 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
[tex]\[
= 6x^2 + (-21x) + (-10x) + 35
\][/tex]
3. Combine the like terms (the [tex]\(x\)[/tex] terms):
[tex]\[
= 6x^2 - 21x - 10x + 35
\][/tex]
[tex]\[
= 6x^2 - 31x + 35
\][/tex]
So the expression that matches the expanded product of [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct answer is:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
