Answer :
Sure, let's find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex] step by step.
1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
This means we'll apply the distributive property:
[tex]\[
= 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
2. Multiply each pair of terms:
[tex]\[
= 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
- First term: [tex]\(3x \cdot 2x = 6x^2\)[/tex]
- Second term: [tex]\(3x \cdot (-7) = -21x\)[/tex]
- Third term: [tex]\((-5) \cdot 2x = -10x\)[/tex]
- Fourth term: [tex]\((-5) \cdot (-7) = 35\)[/tex]
3. Combine all the terms together:
[tex]\[
= 6x^2 - 21x - 10x + 35
\][/tex]
4. Combine like terms:
[tex]\[
-21x - 10x = -31x
\][/tex]
Therefore, the expression becomes:
[tex]\[
= 6x^2 - 31x + 35
\][/tex]
Now we can compare this to the given choices:
- [tex]\(6x^2 - 31x - 12\)[/tex]
- [tex]\(6x^2 + 31x - 35\)[/tex]
- [tex]\(6x^2 - 31x + 35\)[/tex]
- [tex]\(5x^2 - 21x + 12\)[/tex]
The correct expression is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is equal to [tex]\(6x^2 - 31x + 35\)[/tex].
1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
This means we'll apply the distributive property:
[tex]\[
= 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
2. Multiply each pair of terms:
[tex]\[
= 3x \cdot 2x + 3x \cdot (-7) + (-5) \cdot 2x + (-5) \cdot (-7)
\][/tex]
- First term: [tex]\(3x \cdot 2x = 6x^2\)[/tex]
- Second term: [tex]\(3x \cdot (-7) = -21x\)[/tex]
- Third term: [tex]\((-5) \cdot 2x = -10x\)[/tex]
- Fourth term: [tex]\((-5) \cdot (-7) = 35\)[/tex]
3. Combine all the terms together:
[tex]\[
= 6x^2 - 21x - 10x + 35
\][/tex]
4. Combine like terms:
[tex]\[
-21x - 10x = -31x
\][/tex]
Therefore, the expression becomes:
[tex]\[
= 6x^2 - 31x + 35
\][/tex]
Now we can compare this to the given choices:
- [tex]\(6x^2 - 31x - 12\)[/tex]
- [tex]\(6x^2 + 31x - 35\)[/tex]
- [tex]\(6x^2 - 31x + 35\)[/tex]
- [tex]\(5x^2 - 21x + 12\)[/tex]
The correct expression is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is equal to [tex]\(6x^2 - 31x + 35\)[/tex].
