Answer :
To solve the problem of finding which expression is equal to [tex]\((3x-5)(2x-7)\)[/tex], we need to expand the expression by multiplying the two binomials.
Here’s a step-by-step walkthrough:
1. Distribute Each Term: You start by distributing each term in the first binomial across the second binomial.
- Multiply the first term from the first binomial [tex]\(3x\)[/tex] with each term in the second binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
- Multiply the second term from the first binomial [tex]\(-5\)[/tex] with each term in the second binomial:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
2. Combine Like Terms: Next, combine the like terms from the products we calculated above.
- You have the terms: [tex]\(6x^2\)[/tex], [tex]\(-21x\)[/tex], [tex]\(-10x\)[/tex], and [tex]\(35\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-21x + (-10x) = -31x\)[/tex].
3. Write the Expanded Expression: Now, write out the expanded and simplified expression:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Based on these calculations, the expression [tex]\((3x-5)(2x-7)\)[/tex] is simplified to [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct answer is the expression:
[tex]\(6x^2 - 31x + 35\)[/tex].
Here’s a step-by-step walkthrough:
1. Distribute Each Term: You start by distributing each term in the first binomial across the second binomial.
- Multiply the first term from the first binomial [tex]\(3x\)[/tex] with each term in the second binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
[tex]\[
3x \cdot (-7) = -21x
\][/tex]
- Multiply the second term from the first binomial [tex]\(-5\)[/tex] with each term in the second binomial:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
[tex]\[
-5 \cdot (-7) = 35
\][/tex]
2. Combine Like Terms: Next, combine the like terms from the products we calculated above.
- You have the terms: [tex]\(6x^2\)[/tex], [tex]\(-21x\)[/tex], [tex]\(-10x\)[/tex], and [tex]\(35\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-21x + (-10x) = -31x\)[/tex].
3. Write the Expanded Expression: Now, write out the expanded and simplified expression:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Based on these calculations, the expression [tex]\((3x-5)(2x-7)\)[/tex] is simplified to [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct answer is the expression:
[tex]\(6x^2 - 31x + 35\)[/tex].
