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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 - 34x + 35[/tex]

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

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

Answer :

To find the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we'll perform the multiplication step-by-step:

1. Multiply the first term in the first binomial by each term in the second binomial:

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

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

2. Multiply the second term in the first binomial by each term in the second binomial:

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

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

3. Add all the results together:

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

4. Combine like terms:

The like terms in this expression are [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]. Add them together:

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

5. Write the final quadratic expression:

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

Therefore, the quadratic expression that represents the product is:

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

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

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