College

Select the correct answer.

Which quadratic expression represents the product of these factors?
[tex] (2x+5)(7-4x) [/tex]

A. [tex] -8x^2-6x+35 [/tex]
B. [tex] -8x^2-34x+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 factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we'll follow these steps using the distributive property method (often known as the FOIL method):

1. First: Multiply the first terms in each binomial:
[tex]\(2x \times 7 = 14x\)[/tex].

2. Outer: Multiply the outer terms in the binomial:
[tex]\(2x \times (-4x) = -8x^2\)[/tex].

3. Inner: Multiply the inner terms in the binomial:
[tex]\(5 \times 7 = 35\)[/tex].

4. Last: Multiply the last terms in each binomial:
[tex]\(5 \times (-4x) = -20x\)[/tex].

Now combine all these results:
[tex]\(-8x^2 + 14x - 20x + 35\)[/tex].

Next, simplify by combining like terms:
[tex]\(-8x^2 + (14x - 20x) + 35 = -8x^2 - 6x + 35\)[/tex].

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

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