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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 find the quadratic expression that represents the product of the given factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we need to use the distributive property, often called the FOIL method (First, Outside, Inside, Last) for binomials. Here is the step-by-step solution:

1. Multiply the First terms:

[tex]\((2x) \times (7) = 14x\)[/tex]

2. Multiply the Outside terms:

[tex]\((2x) \times (-4x) = -8x^2\)[/tex]

3. Multiply the Inside terms:

[tex]\((5) \times (7) = 35\)[/tex]

4. Multiply the Last terms:

[tex]\((5) \times (-4x) = -20x\)[/tex]

5. Combine all these products:

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

6. Combine like terms:

Combine the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex]

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

Thus, the quadratic expression that represents the product is [tex]\(-8x^2 - 6x + 35\)[/tex].

From the given options, the correct answer is:

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

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