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

Answer :

To find the quadratic expression that represents the product of the factors [tex]\( (2x + 5)(7 - 4x) \)[/tex], we can use the distributive property, also known as the FOIL method (First, Outside, Inside, Last). Let's multiply each term in the first binomial by each term in the second binomial:

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

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

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

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

Now, we will combine the like terms:

- The [tex]\(x^2\)[/tex] terms: [tex]\(-8x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex].
- The constant term: [tex]\(+35\)[/tex].

Putting it all together, the quadratic expression is:
[tex]\[ -8x^2 - 6x + 35 \][/tex]

So, the correct answer is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].

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