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Answer :
To solve the problem of finding which quadratic expression represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we can use the distributive property, also known as the FOIL method (First, Outside, Inside, Last), to expand the expression. Let's go through the steps to expand these factors:
1. First terms: Multiply the first terms in each binomial.
[tex]\[
2x \cdot 7 = 14x
\][/tex]
2. Outside terms: Multiply the outer terms in the binomial.
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
3. Inside terms: Multiply the inner terms in the binomial.
[tex]\[
5 \cdot 7 = 35
\][/tex]
4. Last terms: Multiply the last terms in each binomial.
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
Next, let's combine all these results to form a single expression:
- Combine the quadratic term: [tex]\( -8x^2 \)[/tex]
- Combine the linear terms: [tex]\( 14x - 20x = -6x \)[/tex]
- Use the constant term: [tex]\( 35 \)[/tex]
Putting it all together, the expanded quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So, the answer is option A: [tex]\(-8x^2 - 6x + 35\)[/tex].
1. First terms: Multiply the first terms in each binomial.
[tex]\[
2x \cdot 7 = 14x
\][/tex]
2. Outside terms: Multiply the outer terms in the binomial.
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
3. Inside terms: Multiply the inner terms in the binomial.
[tex]\[
5 \cdot 7 = 35
\][/tex]
4. Last terms: Multiply the last terms in each binomial.
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
Next, let's combine all these results to form a single expression:
- Combine the quadratic term: [tex]\( -8x^2 \)[/tex]
- Combine the linear terms: [tex]\( 14x - 20x = -6x \)[/tex]
- Use the constant term: [tex]\( 35 \)[/tex]
Putting it all together, the expanded quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
So, the answer is option A: [tex]\(-8x^2 - 6x + 35\)[/tex].
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