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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].
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].
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