Answer :
To find which expression is equal to [tex]\((3x-5)(2x-7)\)[/tex], let's multiply these two binomials using the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
1. First: Multiply the first terms in each binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
4. Last: Multiply the last terms:
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
Now, combine all these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Combine like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression equivalent to [tex]\((3x-5)(2x-7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct choice is: [tex]\(6x^2 - 31x + 35\)[/tex].
1. First: Multiply the first terms in each binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
4. Last: Multiply the last terms:
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
Now, combine all these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Combine like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression equivalent to [tex]\((3x-5)(2x-7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct choice is: [tex]\(6x^2 - 31x + 35\)[/tex].
