College

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

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

Answer :

Sure! Let's solve the expression [tex]\((3x - 5)(2x - 7)\)[/tex] step-by-step.

First, we will use the distributive property (also known as the FOIL method for binomials) to expand the product of the two binomials:

[tex]\[
(3x - 5)(2x - 7)
\][/tex]

### Step 1: Multiply the First terms
The first terms are [tex]\(3x\)[/tex] and [tex]\(2x\)[/tex]:

[tex]\[
3x \cdot 2x = 6x^2
\][/tex]

### Step 2: Multiply the Outer terms
The outer terms are [tex]\(3x\)[/tex] and [tex]\(-7\)[/tex]:

[tex]\[
3x \cdot (-7) = -21x
\][/tex]

### Step 3: Multiply the Inner terms
The inner terms are [tex]\(-5\)[/tex] and [tex]\(2x\)[/tex]:

[tex]\[
-5 \cdot 2x = -10x
\][/tex]

### Step 4: Multiply the Last terms
The last terms are [tex]\(-5\)[/tex] and [tex]\(-7\)[/tex]:

[tex]\[
-5 \cdot (-7) = 35
\][/tex]

### Step 5: Combine the results
Now, we combine all these results together:

[tex]\[
6x^2 - 21x - 10x + 35
\][/tex]

Combine like terms ([tex]\(-21x - 10x = -31x\)[/tex]):

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

So the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is equal to:

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

Among the given options, the correct expression that matches this result is:

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

Therefore, the correct answer is:

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