Answer :
To find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], let's use the distributive property, often known as the FOIL method (First, Outer, Inner, Last).
Step 1: Multiply the First terms.
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
Step 2: Multiply the Outer terms.
[tex]\[
3x \cdot -7 = -21x
\][/tex]
Step 3: Multiply the Inner terms.
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
Step 4: Multiply the Last terms.
[tex]\[
-5 \cdot -7 = 35
\][/tex]
Step 5: Add all the products together:
[tex]\[
6x^2 + (-21x) + (-10x) + 35
\][/tex]
Step 6: Combine like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct choice is:
[tex]\[
\boxed{6x^2 - 31x + 35}
\][/tex]
Step 1: Multiply the First terms.
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
Step 2: Multiply the Outer terms.
[tex]\[
3x \cdot -7 = -21x
\][/tex]
Step 3: Multiply the Inner terms.
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
Step 4: Multiply the Last terms.
[tex]\[
-5 \cdot -7 = 35
\][/tex]
Step 5: Add all the products together:
[tex]\[
6x^2 + (-21x) + (-10x) + 35
\][/tex]
Step 6: Combine like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct choice is:
[tex]\[
\boxed{6x^2 - 31x + 35}
\][/tex]
