High School

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 determine which quadratic expression represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we need to expand the expression step-by-step. Here's how you can do it:

1. Apply the distributive property (FOIL method):
[tex]\[
(2x + 5)(7 - 4x)
\][/tex]
We'll break it down into four parts:

- First: [tex]\(2x \cdot 7 = 14x\)[/tex]
- Outer: [tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
- Inner: [tex]\(5 \cdot 7 = 35\)[/tex]
- Last: [tex]\(5 \cdot (-4x) = -20x\)[/tex]

2. Combine these parts together:
[tex]\[
14x - 8x^2 + 35 - 20x
\][/tex]

3. Simplify by combining like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex]
- No other like terms to combine, so we rewrite the expression:

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

So the quadratic expression representing the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:

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

Now, let's match this result to one of the given answer choices:

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]

The expression we derived is [tex]\(-8x^2 - 6x + 35\)[/tex], which corresponds to option B.

Thus, the correct answer is:
[tex]\[
\boxed{B}
\][/tex]

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