Answer :
To find the quadratic expression that 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). Let's multiply each term in the first binomial by each term in the second binomial:
1. First: Multiply the first terms of each binomial:
[tex]\((2x) \times (7) = 14x\)[/tex].
2. Outside: Multiply the outer terms of the binomials:
[tex]\((2x) \times (-4x) = -8x^2\)[/tex].
3. Inside: Multiply the inner terms of the binomials:
[tex]\((5) \times (7) = 35\)[/tex].
4. Last: Multiply the last terms of each binomial:
[tex]\((5) \times (-4x) = -20x\)[/tex].
Now, we will combine the like terms:
- The [tex]\(x^2\)[/tex] terms: [tex]\(-8x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex].
- The constant term: [tex]\(+35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[ -8x^2 - 6x + 35 \][/tex]
So, the correct answer is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
1. First: Multiply the first terms of each binomial:
[tex]\((2x) \times (7) = 14x\)[/tex].
2. Outside: Multiply the outer terms of the binomials:
[tex]\((2x) \times (-4x) = -8x^2\)[/tex].
3. Inside: Multiply the inner terms of the binomials:
[tex]\((5) \times (7) = 35\)[/tex].
4. Last: Multiply the last terms of each binomial:
[tex]\((5) \times (-4x) = -20x\)[/tex].
Now, we will combine the like terms:
- The [tex]\(x^2\)[/tex] terms: [tex]\(-8x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex].
- The constant term: [tex]\(+35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[ -8x^2 - 6x + 35 \][/tex]
So, the correct answer is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
