Answer :
To find the quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex], follow these steps:
1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[
(2x + 5)(7 - 4x) = (2x \cdot 7) + (2x \cdot -4x) + (5 \cdot 7) + (5 \cdot -4x)
\][/tex]
2. Calculate each product:
- [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. Rearrange the terms to standard quadratic form [tex]\(ax^2 + bx + c\)[/tex]:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
5. Combine like terms:
- Combine [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex] to get [tex]\(-6x\)[/tex]
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Thus, 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:
C. [tex]\(-8x^2 + 6x - 35\)[/tex]
1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[
(2x + 5)(7 - 4x) = (2x \cdot 7) + (2x \cdot -4x) + (5 \cdot 7) + (5 \cdot -4x)
\][/tex]
2. Calculate each product:
- [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. Rearrange the terms to standard quadratic form [tex]\(ax^2 + bx + c\)[/tex]:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
5. Combine like terms:
- Combine [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex] to get [tex]\(-6x\)[/tex]
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Thus, 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:
C. [tex]\(-8x^2 + 6x - 35\)[/tex]
