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Answer :
To find the quadratic expression that represents the product of the factors [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex], we can expand the expression step by step:
1. Multiply each term in the first bracket by each term in the second bracket.
[tex]\((2x + 5) \cdot (7 - 4x)\)[/tex]
2. Distribute the terms:
- Multiply [tex]\(2x\)[/tex] by [tex]\(7\)[/tex]:
[tex]\[
2x \times 7 = 14x
\][/tex]
- Multiply [tex]\(2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
2x \times -4x = -8x^2
\][/tex]
- Multiply [tex]\(5\)[/tex] by [tex]\(7\)[/tex]:
[tex]\[
5 \times 7 = 35
\][/tex]
- Multiply [tex]\(5\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
5 \times -4x = -20x
\][/tex]
3. Combine all the results:
Put together all the terms we calculated:
[tex]\[
14x + (-8x^2) + 35 + (-20x) = -8x^2 + (14x - 20x) + 35
\][/tex]
4. Simplify the expression:
Combine the like terms:
[tex]\[
14x - 20x = -6x
\][/tex]
So, the expression becomes:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
The quadratic expression is [tex]\(-8x^2 - 6x + 35\)[/tex].
Therefore, the correct answer is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
1. Multiply each term in the first bracket by each term in the second bracket.
[tex]\((2x + 5) \cdot (7 - 4x)\)[/tex]
2. Distribute the terms:
- Multiply [tex]\(2x\)[/tex] by [tex]\(7\)[/tex]:
[tex]\[
2x \times 7 = 14x
\][/tex]
- Multiply [tex]\(2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
2x \times -4x = -8x^2
\][/tex]
- Multiply [tex]\(5\)[/tex] by [tex]\(7\)[/tex]:
[tex]\[
5 \times 7 = 35
\][/tex]
- Multiply [tex]\(5\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
5 \times -4x = -20x
\][/tex]
3. Combine all the results:
Put together all the terms we calculated:
[tex]\[
14x + (-8x^2) + 35 + (-20x) = -8x^2 + (14x - 20x) + 35
\][/tex]
4. Simplify the expression:
Combine the like terms:
[tex]\[
14x - 20x = -6x
\][/tex]
So, the expression becomes:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
The quadratic expression is [tex]\(-8x^2 - 6x + 35\)[/tex].
Therefore, the correct answer is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
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