Answer :
Sure, let's work through the problem step by step to find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex].
We'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):
1. First:
[tex]\(3x \cdot 2x = 6x^2\)[/tex]
2. Outer:
[tex]\(3x \cdot (-7) = -21x\)[/tex]
3. Inner:
[tex]\(-5 \cdot 2x = -10x\)[/tex]
4. Last:
[tex]\(-5 \cdot (-7) = 35\)[/tex]
Now we'll add all these parts together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Next, combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] expands to [tex]\(6x^2 - 31x + 35\)[/tex].
Looking at the given options:
[tex]\[
1. 6x^2 + 31x - 35
\][/tex]
[tex]\[
2. 6x^2 - 31x - 12
\][/tex]
[tex]\[
3. 5x^2 - 21x + 12
\][/tex]
[tex]\[
4. 6x^2 - 31x + 35
\][/tex]
The correct expression is [tex]\(6x^2 - 31x + 35\)[/tex], which matches option 4.
So, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
We'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):
1. First:
[tex]\(3x \cdot 2x = 6x^2\)[/tex]
2. Outer:
[tex]\(3x \cdot (-7) = -21x\)[/tex]
3. Inner:
[tex]\(-5 \cdot 2x = -10x\)[/tex]
4. Last:
[tex]\(-5 \cdot (-7) = 35\)[/tex]
Now we'll add all these parts together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Next, combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] expands to [tex]\(6x^2 - 31x + 35\)[/tex].
Looking at the given options:
[tex]\[
1. 6x^2 + 31x - 35
\][/tex]
[tex]\[
2. 6x^2 - 31x - 12
\][/tex]
[tex]\[
3. 5x^2 - 21x + 12
\][/tex]
[tex]\[
4. 6x^2 - 31x + 35
\][/tex]
The correct expression is [tex]\(6x^2 - 31x + 35\)[/tex], which matches option 4.
So, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
