Answer :
Sure! Let's find which given expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex] by expanding the expression step by step.
We start with the expression:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
To expand it, we will use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):
1. First: Multiply the first terms in each binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
3x \cdot -7 = -21x
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-5 \cdot -7 = 35
\][/tex]
Now, combine all these products:
[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]
Hence, the expanded form of [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Now, let's compare this result with the given options:
1. [tex]\(6x^2 - 31x + 35\)[/tex]
2. [tex]\(6x^2 - 31x - 12\)[/tex]
3. [tex]\(5x^2 - 21x + 12\)[/tex]
4. [tex]\(6x^2 + 31x - 35\)[/tex]
The correct expression that matches [tex]\(6x^2 - 31x + 35\)[/tex] is the first option:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{6x^2 - 31x + 35}
\][/tex]
We start with the expression:
[tex]\[
(3x - 5)(2x - 7)
\][/tex]
To expand it, we will use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):
1. First: Multiply the first terms in each binomial:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
3x \cdot -7 = -21x
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
-5 \cdot 2x = -10x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-5 \cdot -7 = 35
\][/tex]
Now, combine all these products:
[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]
Hence, the expanded form of [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Now, let's compare this result with the given options:
1. [tex]\(6x^2 - 31x + 35\)[/tex]
2. [tex]\(6x^2 - 31x - 12\)[/tex]
3. [tex]\(5x^2 - 21x + 12\)[/tex]
4. [tex]\(6x^2 + 31x - 35\)[/tex]
The correct expression that matches [tex]\(6x^2 - 31x + 35\)[/tex] is the first option:
[tex]\[
6x^2 - 31x + 35
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{6x^2 - 31x + 35}
\][/tex]
