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Answer :
Sure, let's work through the problem step-by-step.
We need to multiply the two binomials [tex]\((3x-5)(2x-7)\)[/tex]. To do this, we'll use the distributive property (also known as the FOIL method for binomials). The FOIL method stands for First, Outer, Inner, Last, which refers to the terms we need to multiply:
1. First: Multiply the first terms in each binomial:
[tex]\[
(3x) \cdot (2x) = 6x^2
\][/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\[
(3x) \cdot (-7) = -21x
\][/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\[
(-5) \cdot (2x) = -10x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
(-5) \cdot (-7) = 35
\][/tex]
Now, we add all these results together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression [tex]\((3x-5)(2x-7)\)[/tex] expands to:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
The expression corresponding to this result is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
We need to multiply the two binomials [tex]\((3x-5)(2x-7)\)[/tex]. To do this, we'll use the distributive property (also known as the FOIL method for binomials). The FOIL method stands for First, Outer, Inner, Last, which refers to the terms we need to multiply:
1. First: Multiply the first terms in each binomial:
[tex]\[
(3x) \cdot (2x) = 6x^2
\][/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\[
(3x) \cdot (-7) = -21x
\][/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\[
(-5) \cdot (2x) = -10x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
(-5) \cdot (-7) = 35
\][/tex]
Now, we add all these results together:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]
So, the expression [tex]\((3x-5)(2x-7)\)[/tex] expands to:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
The expression corresponding to this result is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
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