Answer :
To find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], let's simplify the given expression step-by-step.
1. Apply the distributive property (also known as the FOIL method):
- First: Multiply the first terms in each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]
- Outer: Multiply the outer terms:
[tex]\[
3x \times -7 = -21x
\][/tex]
- Inner: Multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]
- Last: Multiply the last terms in each binomial:
[tex]\[
-5 \times -7 = 35
\][/tex]
2. Combine all these results:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
3. Combine like terms:
[tex]\[
6x^2 + (-21x - 10x) + 35 = 6x^2 - 31x + 35
\][/tex]
Therefore, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] simplifies to [tex]\(6x^2 - 31x + 35\)[/tex].
Looking at the options provided, the correct choice is:
- [tex]\(6x^2 - 31x + 35\)[/tex]
1. Apply the distributive property (also known as the FOIL method):
- First: Multiply the first terms in each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]
- Outer: Multiply the outer terms:
[tex]\[
3x \times -7 = -21x
\][/tex]
- Inner: Multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]
- Last: Multiply the last terms in each binomial:
[tex]\[
-5 \times -7 = 35
\][/tex]
2. Combine all these results:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
3. Combine like terms:
[tex]\[
6x^2 + (-21x - 10x) + 35 = 6x^2 - 31x + 35
\][/tex]
Therefore, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] simplifies to [tex]\(6x^2 - 31x + 35\)[/tex].
Looking at the options provided, the correct choice is:
- [tex]\(6x^2 - 31x + 35\)[/tex]
