Answer :
To solve the problem of finding the quadratic expression that represents the product [tex]\((2x + 5)(7 - 4x)\)[/tex], we need to expand the expression. Here's a step-by-step explanation:
1. Use the Distributive Property (FOIL Method):
The expression [tex]\((2x + 5)(7 - 4x)\)[/tex] should be expanded by multiplying each term in the first parenthesis by each term in the second parenthesis.
2. Multiply each term:
- [tex]\(2x \times 7 = 14x\)[/tex]
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
- [tex]\(5 \times 7 = 35\)[/tex]
- [tex]\(5 \times (-4x) = -20x\)[/tex]
3. Combine the like terms:
- For the [tex]\(x^2\)[/tex] term, there's only one: [tex]\(-8x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex].
- For the constant term, we have [tex]\(35\)[/tex].
4. Write the final expression:
Combine everything to get the quadratic expression: [tex]\(-8x^2 - 6x + 35\)[/tex].
Thus, the expression that represents the product [tex]\((2x + 5)(7 - 4x)\)[/tex] is [tex]\(-8x^2 - 6x + 35\)[/tex], which matches option A.
1. Use the Distributive Property (FOIL Method):
The expression [tex]\((2x + 5)(7 - 4x)\)[/tex] should be expanded by multiplying each term in the first parenthesis by each term in the second parenthesis.
2. Multiply each term:
- [tex]\(2x \times 7 = 14x\)[/tex]
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]
- [tex]\(5 \times 7 = 35\)[/tex]
- [tex]\(5 \times (-4x) = -20x\)[/tex]
3. Combine the like terms:
- For the [tex]\(x^2\)[/tex] term, there's only one: [tex]\(-8x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex].
- For the constant term, we have [tex]\(35\)[/tex].
4. Write the final expression:
Combine everything to get the quadratic expression: [tex]\(-8x^2 - 6x + 35\)[/tex].
Thus, the expression that represents the product [tex]\((2x + 5)(7 - 4x)\)[/tex] is [tex]\(-8x^2 - 6x + 35\)[/tex], which matches option A.
