Answer :
To find the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], let's go through the multiplication step-by-step.
1. Distribute each term in the first factor to each term in the second factor using the distributive property (also known as the FOIL method for binomials):
[tex]\[
(2x + 5)(7 - 4x)
\][/tex]
First, distribute [tex]\(2x\)[/tex]:
[tex]\[
2x \cdot 7 + 2x \cdot (-4x)
\][/tex]
Then, distribute [tex]\(5\)[/tex]:
[tex]\[
5 \cdot 7 + 5 \cdot (-4x)
\][/tex]
2. Calculate each term:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
[tex]\[
5 \cdot 7 = 35
\][/tex]
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
3. Combine all the terms:
[tex]\[
14x - 8x^2 + 35 - 20x
\][/tex]
4. Combine like terms:
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
14x - 20x = -6x
\][/tex]
So the expression becomes:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Therefore, the quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
[tex]\[
\boxed{-8x^2 - 6x + 35}
\][/tex]
The correct answer is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
1. Distribute each term in the first factor to each term in the second factor using the distributive property (also known as the FOIL method for binomials):
[tex]\[
(2x + 5)(7 - 4x)
\][/tex]
First, distribute [tex]\(2x\)[/tex]:
[tex]\[
2x \cdot 7 + 2x \cdot (-4x)
\][/tex]
Then, distribute [tex]\(5\)[/tex]:
[tex]\[
5 \cdot 7 + 5 \cdot (-4x)
\][/tex]
2. Calculate each term:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
[tex]\[
5 \cdot 7 = 35
\][/tex]
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
3. Combine all the terms:
[tex]\[
14x - 8x^2 + 35 - 20x
\][/tex]
4. Combine like terms:
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
14x - 20x = -6x
\][/tex]
So the expression becomes:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Therefore, the quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
[tex]\[
\boxed{-8x^2 - 6x + 35}
\][/tex]
The correct answer is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
