Answer :
Sure! Let's find the product of the factors [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex] step-by-step using the distributive property, also known as the FOIL method (First, Outside, Inside, Last).
1. First: Multiply the first terms in each binomial:
[tex]\(2x \cdot 7 = 14x\)[/tex]
2. Outside: Multiply the outer terms in the binomials:
[tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
3. Inside: Multiply the inner terms in the binomials:
[tex]\(5 \cdot 7 = 35\)[/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\(5 \cdot (-4x) = -20x\)[/tex]
Now, add all the terms together:
[tex]\[-8x^2 + 14x + 35 - 20x\][/tex]
Combine the like terms [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]:
[tex]\[-8x^2 + (14x - 20x) + 35 = -8x^2 - 6x + 35\][/tex]
Therefore, the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
1. First: Multiply the first terms in each binomial:
[tex]\(2x \cdot 7 = 14x\)[/tex]
2. Outside: Multiply the outer terms in the binomials:
[tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
3. Inside: Multiply the inner terms in the binomials:
[tex]\(5 \cdot 7 = 35\)[/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\(5 \cdot (-4x) = -20x\)[/tex]
Now, add all the terms together:
[tex]\[-8x^2 + 14x + 35 - 20x\][/tex]
Combine the like terms [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]:
[tex]\[-8x^2 + (14x - 20x) + 35 = -8x^2 - 6x + 35\][/tex]
Therefore, the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
