Answer :
Let's solve the problem step by step:
We want to multiply the two binomials: [tex]\((2x + 5)(7 - 4x)\)[/tex].
1. Use the Distributive Property (FOIL method):
Multiply each term in the first binomial by each term in the second binomial:
- First terms: Multiply the first terms in each binomial:
[tex]\(2x \cdot 7 = 14x\)[/tex]
- Outer terms: Multiply the outer terms:
[tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
- Inner terms: Multiply the inner terms:
[tex]\(5 \cdot 7 = 35\)[/tex]
- Last terms: Multiply the last terms:
[tex]\(5 \cdot (-4x) = -20x\)[/tex]
2. Combine like terms:
Add the results from the four steps:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[14x - 20x = -6x\][/tex]
The final expression is:
[tex]\[-8x^2 - 6x + 35\][/tex]
3. Identify the correct expression from the options:
Look for the expression that matches [tex]\(-8x^2 - 6x + 35\)[/tex]:
- A. [tex]\(-8x^2 + 34x - 35\)[/tex]
- B. [tex]\(-8x^2 - 6x + 35\)[/tex]
- C. [tex]\(-8x^2 + 6x - 35\)[/tex]
- D. [tex]\(-8x^2 - 34x + 35\)[/tex]
The correct quadratic expression that represents the product of the given factors is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
We want to multiply the two binomials: [tex]\((2x + 5)(7 - 4x)\)[/tex].
1. Use the Distributive Property (FOIL method):
Multiply each term in the first binomial by each term in the second binomial:
- First terms: Multiply the first terms in each binomial:
[tex]\(2x \cdot 7 = 14x\)[/tex]
- Outer terms: Multiply the outer terms:
[tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
- Inner terms: Multiply the inner terms:
[tex]\(5 \cdot 7 = 35\)[/tex]
- Last terms: Multiply the last terms:
[tex]\(5 \cdot (-4x) = -20x\)[/tex]
2. Combine like terms:
Add the results from the four steps:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[14x - 20x = -6x\][/tex]
The final expression is:
[tex]\[-8x^2 - 6x + 35\][/tex]
3. Identify the correct expression from the options:
Look for the expression that matches [tex]\(-8x^2 - 6x + 35\)[/tex]:
- A. [tex]\(-8x^2 + 34x - 35\)[/tex]
- B. [tex]\(-8x^2 - 6x + 35\)[/tex]
- C. [tex]\(-8x^2 + 6x - 35\)[/tex]
- D. [tex]\(-8x^2 - 34x + 35\)[/tex]
The correct quadratic expression that represents the product of the given factors is option B: [tex]\(-8x^2 - 6x + 35\)[/tex].
