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Answer :
Let's find the product of the factors [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex] step-by-step using the distributive property (also known as the FOIL method).
First, we use the FOIL method, which stands for First, Outer, Inner, Last:
1. First: Multiply the first terms in each binomial:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
5 \cdot 7 = 35
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
Next, we add all these products together:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
Now, combine the like terms ([tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]):
[tex]\[
-8x^2 + (14x - 20x) + 35 = -8x^2 - 6x + 35
\][/tex]
Thus, the quadratic expression representing the product of [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex] is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{-8x^2 - 6x + 35}
\][/tex]
Therefore, the correct answer is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
First, we use the FOIL method, which stands for First, Outer, Inner, Last:
1. First: Multiply the first terms in each binomial:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
5 \cdot 7 = 35
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
Next, we add all these products together:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
Now, combine the like terms ([tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]):
[tex]\[
-8x^2 + (14x - 20x) + 35 = -8x^2 - 6x + 35
\][/tex]
Thus, the quadratic expression representing the product of [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex] is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{-8x^2 - 6x + 35}
\][/tex]
Therefore, the correct answer is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
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