College

Which expression is equal to [tex]$(3x-5)(2x-7)$[/tex]?

A. [tex]6x^2-31x+35[/tex]
B. [tex]6x^2+31x-35[/tex]
C. [tex]5x^2-21x+12[/tex]
D. [tex]6x^2-31x-12[/tex]

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].