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Answer :
To find the product of the factors
[tex]$$ (2x+5)(7-4x), $$[/tex]
we apply the distributive property (also known as the FOIL method). Here are the steps:
1. Multiply the first term of the first factor by each term of the second factor:
- [tex]$$ 2x \cdot 7 = 14x $$[/tex]
- [tex]$$ 2x \cdot (-4x) = -8x^2 $$[/tex]
2. Multiply the second term of the first factor by each term of the second factor:
- [tex]$$ 5 \cdot 7 = 35 $$[/tex]
- [tex]$$ 5 \cdot (-4x) = -20x $$[/tex]
3. Combine the like terms (the [tex]$x$[/tex] terms):
- From step 1 and step 2, the [tex]$x$[/tex] terms are: [tex]$$ 14x \text{ and } -20x $$[/tex]
- Adding them gives: [tex]$$ 14x - 20x = -6x $$[/tex]
4. Write the final expanded quadratic expression:
- The [tex]$x^2$[/tex] term is: [tex]$$ -8x^2 $$[/tex]
- The [tex]$x$[/tex] term is: [tex]$$ -6x $$[/tex]
- The constant term is: [tex]$$ 35 $$[/tex]
Thus, the product is:
[tex]$$ -8x^2 - 6x + 35. $$[/tex]
Comparing with the given options, we see that option A is:
[tex]$$ -8x^2 - 6x + 35. $$[/tex]
So, the correct answer is option A.
[tex]$$ (2x+5)(7-4x), $$[/tex]
we apply the distributive property (also known as the FOIL method). Here are the steps:
1. Multiply the first term of the first factor by each term of the second factor:
- [tex]$$ 2x \cdot 7 = 14x $$[/tex]
- [tex]$$ 2x \cdot (-4x) = -8x^2 $$[/tex]
2. Multiply the second term of the first factor by each term of the second factor:
- [tex]$$ 5 \cdot 7 = 35 $$[/tex]
- [tex]$$ 5 \cdot (-4x) = -20x $$[/tex]
3. Combine the like terms (the [tex]$x$[/tex] terms):
- From step 1 and step 2, the [tex]$x$[/tex] terms are: [tex]$$ 14x \text{ and } -20x $$[/tex]
- Adding them gives: [tex]$$ 14x - 20x = -6x $$[/tex]
4. Write the final expanded quadratic expression:
- The [tex]$x^2$[/tex] term is: [tex]$$ -8x^2 $$[/tex]
- The [tex]$x$[/tex] term is: [tex]$$ -6x $$[/tex]
- The constant term is: [tex]$$ 35 $$[/tex]
Thus, the product is:
[tex]$$ -8x^2 - 6x + 35. $$[/tex]
Comparing with the given options, we see that option A is:
[tex]$$ -8x^2 - 6x + 35. $$[/tex]
So, the correct answer is option A.
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