Answer :
To solve the problem of finding the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], follow these steps:
1. Distribute the terms:
- First, distribute [tex]\(2x\)[/tex] with both terms in the second factor:
[tex]\[
2x \times 7 = 14x
\][/tex]
[tex]\[
2x \times -4x = -8x^2
\][/tex]
- Next, distribute [tex]\(5\)[/tex] with both terms in the second factor:
[tex]\[
5 \times 7 = 35
\][/tex]
[tex]\[
5 \times -4x = -20x
\][/tex]
2. Combine all the terms:
- Now, combine all the results from the distribution:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms ([tex]\(14x - 20x\)[/tex]):
[tex]\[
14x - 20x = -6x
\][/tex]
4. Write the final quadratic expression:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Therefore, the quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is [tex]\(-8x^2 - 6x + 35\)[/tex].
The correct answer is:
D. [tex]\(-8x^2 - 6x + 35\)[/tex]
1. Distribute the terms:
- First, distribute [tex]\(2x\)[/tex] with both terms in the second factor:
[tex]\[
2x \times 7 = 14x
\][/tex]
[tex]\[
2x \times -4x = -8x^2
\][/tex]
- Next, distribute [tex]\(5\)[/tex] with both terms in the second factor:
[tex]\[
5 \times 7 = 35
\][/tex]
[tex]\[
5 \times -4x = -20x
\][/tex]
2. Combine all the terms:
- Now, combine all the results from the distribution:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms ([tex]\(14x - 20x\)[/tex]):
[tex]\[
14x - 20x = -6x
\][/tex]
4. Write the final quadratic expression:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Therefore, the quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is [tex]\(-8x^2 - 6x + 35\)[/tex].
The correct answer is:
D. [tex]\(-8x^2 - 6x + 35\)[/tex]
