Answer :
To determine which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we can expand the given product:
1. Distribute each term in the first binomial to each term in the second binomial:
- First, distribute [tex]\(3x\)[/tex] to both terms in [tex]\(2x - 7\)[/tex]:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
- Next, distribute [tex]\(-5\)[/tex] to both terms in [tex]\(2x - 7\)[/tex]:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
2. Combine all of these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
3. Combine like terms:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expanded expression is [tex]\(6x^2 - 31x + 35\)[/tex].
Let's match this expression with the given options:
1. [tex]\(6x^2 - 31x - 12\)[/tex]
2. [tex]\(5x^2 - 21x + 12\)[/tex]
3. [tex]\(6x^2 - 31x + 35\)[/tex]
4. [tex]\(6x^2 + 31x - 35\)[/tex]
The expression [tex]\(6x^2 - 31x + 35\)[/tex] matches exactly with the third option.
Therefore, the expression that is equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[ \boxed{6x^2 - 31x + 35} \][/tex]
1. Distribute each term in the first binomial to each term in the second binomial:
- First, distribute [tex]\(3x\)[/tex] to both terms in [tex]\(2x - 7\)[/tex]:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
- Next, distribute [tex]\(-5\)[/tex] to both terms in [tex]\(2x - 7\)[/tex]:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
2. Combine all of these products:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
3. Combine like terms:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expanded expression is [tex]\(6x^2 - 31x + 35\)[/tex].
Let's match this expression with the given options:
1. [tex]\(6x^2 - 31x - 12\)[/tex]
2. [tex]\(5x^2 - 21x + 12\)[/tex]
3. [tex]\(6x^2 - 31x + 35\)[/tex]
4. [tex]\(6x^2 + 31x - 35\)[/tex]
The expression [tex]\(6x^2 - 31x + 35\)[/tex] matches exactly with the third option.
Therefore, the expression that is equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[ \boxed{6x^2 - 31x + 35} \][/tex]
