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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 - 6x + 35 [/tex]
B. [tex] -8x^2 + 6x - 35 [/tex]
C. [tex] -8x^2 - 34x + 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, often called the FOIL method for binomials, which stands for First, Outside, Inside, Last. Here's how it works:

1. First Terms:
Multiply the first terms in each binomial:
[tex]\[
2x \times (-4x) = -8x^2
\][/tex]

2. Outside Terms:
Multiply the outside terms:
[tex]\[
2x \times 7 = 14x
\][/tex]

3. Inside Terms:
Multiply the inside terms:
[tex]\[
5 \times (-4x) = -20x
\][/tex]

4. Last Terms:
Multiply the last terms:
[tex]\[
5 \times 7 = 35
\][/tex]

Now, we combine all these results:
- The quadratic term is [tex]\(-8x^2\)[/tex].
- For the linear terms, combine [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]:
[tex]\[
14x - 20x = -6x
\][/tex]
- The constant term is [tex]\(35\)[/tex].

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

Thus, the correct choice from the options is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]

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