Answer :
To solve the problem of finding the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we follow these steps:
1. Apply the Distributive Property: We need to distribute each term in the first parenthesis [tex]\((2x + 5)\)[/tex] to every term in the second parenthesis [tex]\((7 - 4x)\)[/tex].
2. Multiply the First Terms:
- [tex]\(2x \times 7 = 14x\)[/tex]
3. Multiply the Outer Terms:
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
4. Multiply the Inner Terms:
- [tex]\(5 \times 7 = 35\)[/tex]
5. Multiply the Last Terms:
- [tex]\(5 \times (-4x) = -20x\)[/tex]
6. Combine All the Terms:
- You then add all these results together: [tex]\(-8x^2 + 14x + 35 - 20x\)[/tex].
7. Combine Like Terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex]
Putting it all together, the expanded expression becomes:
[tex]\[-8x^2 - 6x + 35\][/tex]
Thus, the quadratic expression representing the product of the given factors is [tex]\(-8x^2 - 6x + 35\)[/tex].
The correct option is:
C. [tex]\(-8x^2 - 6x + 35\)[/tex]
1. Apply the Distributive Property: We need to distribute each term in the first parenthesis [tex]\((2x + 5)\)[/tex] to every term in the second parenthesis [tex]\((7 - 4x)\)[/tex].
2. Multiply the First Terms:
- [tex]\(2x \times 7 = 14x\)[/tex]
3. Multiply the Outer Terms:
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
4. Multiply the Inner Terms:
- [tex]\(5 \times 7 = 35\)[/tex]
5. Multiply the Last Terms:
- [tex]\(5 \times (-4x) = -20x\)[/tex]
6. Combine All the Terms:
- You then add all these results together: [tex]\(-8x^2 + 14x + 35 - 20x\)[/tex].
7. Combine Like Terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex]
Putting it all together, the expanded expression becomes:
[tex]\[-8x^2 - 6x + 35\][/tex]
Thus, the quadratic expression representing the product of the given factors is [tex]\(-8x^2 - 6x + 35\)[/tex].
The correct option is:
C. [tex]\(-8x^2 - 6x + 35\)[/tex]
