Answer :
To determine which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we will expand the given binomials step-by-step.
1. Distribute each term in the first binomial by each term in the second binomial:
[tex]\[(3x - 5)(2x - 7)\][/tex]
2. Multiply each term:
- First, multiply [tex]\(3x\)[/tex] by [tex]\(2x\)[/tex]:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
- Next, multiply [tex]\(3x\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
- Then, multiply [tex]\(-5\)[/tex] by [tex]\(2x\)[/tex]:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
- Finally, multiply [tex]\(-5\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
3. Combine all these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
4. Combine like terms:
[tex]\[
6x^2 - 31x + 35
\][/tex]
After simplifying, we get the expanded expression:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the correct expression that equals [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct option is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
1. Distribute each term in the first binomial by each term in the second binomial:
[tex]\[(3x - 5)(2x - 7)\][/tex]
2. Multiply each term:
- First, multiply [tex]\(3x\)[/tex] by [tex]\(2x\)[/tex]:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
- Next, multiply [tex]\(3x\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
- Then, multiply [tex]\(-5\)[/tex] by [tex]\(2x\)[/tex]:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
- Finally, multiply [tex]\(-5\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
3. Combine all these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
4. Combine like terms:
[tex]\[
6x^2 - 31x + 35
\][/tex]
After simplifying, we get the expanded expression:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the correct expression that equals [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct option is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
