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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]
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]
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