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]
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]
