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

A. [tex]5x^2-21x+12[/tex]

B. [tex]6x^2-31x+35[/tex]

C. [tex]6x^2-31x-12[/tex]

D. [tex]6x^2+31x-35[/tex]

Answer :

Sure! Let's break down the expression [tex]\((3x - 5)(2x - 7)\)[/tex] step-by-step to find out which of the given options it equals.

To start, we will use the distributive property (also known as the FOIL method for binomials) to expand the expression:

1. First terms: Multiply the first terms in each binomial:
[tex]\[
3x \times 2x = 6x^2
\][/tex]

2. Outer terms: Multiply the outer terms in each binomial:
[tex]\[
3x \times -7 = -21x
\][/tex]

3. Inner terms: Multiply the inner terms in each binomial:
[tex]\[
-5 \times 2x = -10x
\][/tex]

4. Last terms: Multiply the last terms in each binomial:
[tex]\[
-5 \times -7 = 35
\][/tex]

Now, we sum all these results:
[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]

Next, combine the like terms [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[
6x^2 - 31x + 35
\][/tex]

So the expanded form of [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]

Thus, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is equal to:
[tex]\[
6x^2 - 31x + 35
\][/tex]

Therefore, the correct option is:
[tex]\[
6 x^2 - 31 x + 35
\][/tex]

Thanks for taking the time to read Which expression is equal to tex 3x 5 2x 7 tex A tex 5x 2 21x 12 tex B tex 6x 2 31x 35 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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