Answer :
To determine which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we need to expand the product:
1. Distribute each term in the first binomial [tex]\((3x - 5)\)[/tex] by each term in the second binomial [tex]\((2x - 7)\)[/tex]:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
2. Multiply [tex]\(3x\)[/tex] by each term in the second binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot -7 = -21x
\][/tex]
3. Now, multiply [tex]\(-5\)[/tex] by each term in the second binomial:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot -7 = 35
\][/tex]
4. Add together all the resulting terms:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
5. Combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expanded form of the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the expression equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Hence, the correct option is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
1. Distribute each term in the first binomial [tex]\((3x - 5)\)[/tex] by each term in the second binomial [tex]\((2x - 7)\)[/tex]:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
2. Multiply [tex]\(3x\)[/tex] by each term in the second binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot -7 = -21x
\][/tex]
3. Now, multiply [tex]\(-5\)[/tex] by each term in the second binomial:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot -7 = 35
\][/tex]
4. Add together all the resulting terms:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
5. Combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expanded form of the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the expression equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Hence, the correct option is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
