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Answer :
To find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we need to expand the expression by using the distributive property, also known as the FOIL method for binomials.
Here's a step-by-step breakdown:
1. First terms: Multiply the first terms of each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]
2. Outer terms: Multiply the outer terms:
[tex]\[
3x \times (-7) = -21x
\][/tex]
3. Inner terms: Multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]
4. Last terms: Multiply the last terms:
[tex]\[
-5 \times (-7) = 35
\][/tex]
Now, combine all these results:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]
This shows that the expression that corresponds to the expanded form of [tex]\((3x - 5)(2x - 7)\)[/tex] is [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Here's a step-by-step breakdown:
1. First terms: Multiply the first terms of each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]
2. Outer terms: Multiply the outer terms:
[tex]\[
3x \times (-7) = -21x
\][/tex]
3. Inner terms: Multiply the inner terms:
[tex]\[
-5 \times 2x = -10x
\][/tex]
4. Last terms: Multiply the last terms:
[tex]\[
-5 \times (-7) = 35
\][/tex]
Now, combine all these results:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]
Combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]
This shows that the expression that corresponds to the expanded form of [tex]\((3x - 5)(2x - 7)\)[/tex] is [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
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