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Answer :
To find the quadratic expression that represents the product of these factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we can use the distributive property, often referred to as the FOIL method in this context. FOIL stands for First, Outer, Inner, Last, which are the terms we will multiply together.
Let's go through the steps:
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, we combine these results to form the quadratic expression:
- The [tex]\(x^2\)[/tex] term is [tex]\(-8x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex].
- The constant term is [tex]\(35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So the correct answer is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
Let's go through the steps:
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, we combine these results to form the quadratic expression:
- The [tex]\(x^2\)[/tex] term is [tex]\(-8x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex].
- The constant term is [tex]\(35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So the correct answer is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
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