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Answer :
To find the product of the factors
[tex]$$ (2x + 5)(7 - 4x), $$[/tex]
we multiply each term in the first factor by each term in the second factor.
1. Multiply the first term in the first factor by each term in the second factor:
- [tex]\(2x \times 7 = 14x\)[/tex]
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
2. Multiply the second term in the first factor by each term in the second factor:
- [tex]\(5 \times 7 = 35\)[/tex]
- [tex]\(5 \times (-4x) = -20x\)[/tex]
3. Now, combine like terms. The [tex]\(x^2\)[/tex] term is:
[tex]$$ -8x^2 $$[/tex]
The [tex]\(x\)[/tex] terms are:
[tex]$$ 14x - 20x = -6x $$[/tex]
The constant term is:
[tex]$$ 35 $$[/tex]
So, the expanded quadratic expression is:
[tex]$$ -8x^2 - 6x + 35. $$[/tex]
Among the given options, the correct answer is:
D. [tex]\( -8x^2 - 6x + 35 \)[/tex].
[tex]$$ (2x + 5)(7 - 4x), $$[/tex]
we multiply each term in the first factor by each term in the second factor.
1. Multiply the first term in the first factor by each term in the second factor:
- [tex]\(2x \times 7 = 14x\)[/tex]
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
2. Multiply the second term in the first factor by each term in the second factor:
- [tex]\(5 \times 7 = 35\)[/tex]
- [tex]\(5 \times (-4x) = -20x\)[/tex]
3. Now, combine like terms. The [tex]\(x^2\)[/tex] term is:
[tex]$$ -8x^2 $$[/tex]
The [tex]\(x\)[/tex] terms are:
[tex]$$ 14x - 20x = -6x $$[/tex]
The constant term is:
[tex]$$ 35 $$[/tex]
So, the expanded quadratic expression is:
[tex]$$ -8x^2 - 6x + 35. $$[/tex]
Among the given options, the correct answer is:
D. [tex]\( -8x^2 - 6x + 35 \)[/tex].
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