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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+34x-35[/tex]

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

Answer :

To determine which quadratic expression represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we'll use the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last).

Here are the steps:

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

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

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

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

Now, add all these products together to form the quadratic expression:

[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]

Next, combine the like terms [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]:

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

The quadratic expression that represents the product of these factors is [tex]\(-8x^2 - 6x + 35\)[/tex].

Looking at the provided options, the correct choice is:

D. [tex]\(-8x^2 - 6x + 35\)[/tex]

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