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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 :

Let's find the quadratic expression that represents the product of [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex].

To multiply these two binomials, we apply the distributive property, also known as the FOIL method (First, Outside, Inside, Last):

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

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

3. Inside: Multiply the inner terms.
[tex]\[
5 \times -4x = -20x
\][/tex]

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

Next, we combine the results from the middle terms (the [tex]\(x\)[/tex] terms):

[tex]\[
14x - 20x = -6x
\][/tex]

Therefore, putting it all together, the product of [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex] is:

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

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

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

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