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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 expand the expression [tex]$$(2x+5)(7-4x),$$[/tex] follow these steps:

1. Multiply [tex]$2x$[/tex] by each term in the second factor:
[tex]$$2x \cdot 7 = 14x,$$[/tex]
[tex]$$2x \cdot (-4x) = -8x^2.$$[/tex]

2. Multiply [tex]$5$[/tex] by each term in the second factor:
[tex]$$5 \cdot 7 = 35,$$[/tex]
[tex]$$5 \cdot (-4x) = -20x.$$[/tex]

3. Combine the like terms:
- The [tex]$x^2$[/tex] term: [tex]$$-8x^2.$$[/tex]
- The [tex]$x$[/tex] terms: [tex]$$14x + (-20x) = -6x.$$[/tex]
- The constant term: [tex]$$35.$$[/tex]

Thus, the expanded form is
[tex]$$-8x^2 - 6x + 35.$$[/tex]

This matches option D.

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