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Answer :
To find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we need to simplify it using the distributive property, also known as the FOIL method. Here is a detailed step-by-step solution:
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]
5. Combine all results: Add all these products together:
[tex]\[
6x^2 + (-21x) + (-10x) + 35
\][/tex]
6. Combine like terms: Add the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[
-21x - 10x = -31x
\][/tex]
7. Final expression: Put it all together:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Comparing this result with the options given, we see that the correct matching expression is:
[tex]\(6x^2 - 31x + 35\)[/tex]
Therefore, [tex]\((3x - 5)(2x - 7) = 6x^2 - 31x + 35\)[/tex].
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]
5. Combine all results: Add all these products together:
[tex]\[
6x^2 + (-21x) + (-10x) + 35
\][/tex]
6. Combine like terms: Add the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[
-21x - 10x = -31x
\][/tex]
7. Final expression: Put it all together:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Comparing this result with the options given, we see that the correct matching expression is:
[tex]\(6x^2 - 31x + 35\)[/tex]
Therefore, [tex]\((3x - 5)(2x - 7) = 6x^2 - 31x + 35\)[/tex].
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