Answer :
Sure! Let's solve the expression [tex]\((3x - 5)(2x - 7)\)[/tex] step-by-step to find which one of the given options it matches.
### Step-by-Step Solution:
1. Distribute each term in the first bracket to each term in the second bracket:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
2. Apply the distributive property (FOIL method):
- First: [tex]\(3x \cdot 2x = 6x^2\)[/tex]
- Outer: [tex]\(3x \cdot (-7) = -21x\)[/tex]
- Inner: [tex]\((-5) \cdot 2x = -10x\)[/tex]
- Last: [tex]\((-5) \cdot (-7) = 35\)[/tex]
3. Combine all the terms together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
4. Combine like terms:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expanded form of [tex]\((3x-5)(2x-7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
### Conclusion:
The expression [tex]\((3x-5)(2x-7)\)[/tex] matches the option:
[tex]\[
\boxed{6x^2 - 31x + 35}
\][/tex]
Thus, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
### Step-by-Step Solution:
1. Distribute each term in the first bracket to each term in the second bracket:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
2. Apply the distributive property (FOIL method):
- First: [tex]\(3x \cdot 2x = 6x^2\)[/tex]
- Outer: [tex]\(3x \cdot (-7) = -21x\)[/tex]
- Inner: [tex]\((-5) \cdot 2x = -10x\)[/tex]
- Last: [tex]\((-5) \cdot (-7) = 35\)[/tex]
3. Combine all the terms together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
4. Combine like terms:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expanded form of [tex]\((3x-5)(2x-7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
### Conclusion:
The expression [tex]\((3x-5)(2x-7)\)[/tex] matches the option:
[tex]\[
\boxed{6x^2 - 31x + 35}
\][/tex]
Thus, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
