High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Select the correct answer.

Which quadratic expression represents the product of these factors?
[tex]$(2x + 5)(7 - 4x)$[/tex]

A. [tex]$-8x^2 - 34x + 35$[/tex]
B. [tex]$-8x^2 + 34x - 35$[/tex]
C. [tex]$-8x^2 + 6x - 35$[/tex]
D. [tex]$-8x^2 - 6x + 35$[/tex]

Answer :

To solve for the product of the quadratic expression [tex]\((2x + 5)(7 - 4x)\)[/tex], let's multiply these two binomials using the distributive property, often remembered as the FOIL method, which stands for First, Outer, Inner, Last:

1. First terms: Multiply the first terms of each binomial:
- [tex]\(2x \times 7 = 14x\)[/tex]

2. Outer terms: Multiply the outer terms of the binomials:
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]

3. Inner terms: Multiply the inner terms of the binomials:
- [tex]\(5 \times 7 = 35\)[/tex]

4. Last terms: Multiply the last terms of each binomial:
- [tex]\(5 \times (-4x) = -20x\)[/tex]

Now, we need to combine all these results:

- Start with the [tex]\(-8x^2\)[/tex].
- The x terms [tex]\(14x - 20x = -6x\)[/tex].
- Lastly, add the constant term [tex]\(35\)[/tex].

Putting it all together, the quadratic expression is:

[tex]\[ -8x^2 - 6x + 35 \][/tex]

Therefore, the correct choice is D: [tex]\(-8x^2 - 6x + 35\)[/tex].