Answer :
To solve the problem of finding the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], follow these steps:
1. Apply the Distributive Property:
The distributive property allows us to multiply each term in the first binomial by each term in the second binomial. It's also known as the FOIL method when dealing with two binomials: First, Outer, Inner, Last.
2. Multiply the First Terms:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
3. Multiply the Outer Terms:
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
4. Multiply the Inner Terms:
[tex]\[
5 \cdot 7 = 35
\][/tex]
5. Multiply the Last Terms:
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
6. Combine Like Terms:
- The terms involving [tex]\(x\)[/tex] are [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]. Combine these to get:
[tex]\[
14x + (-20x) = -6x
\][/tex]
- The constant term remains as [tex]\(35\)[/tex].
7. Write the Final Expression:
By combining all our results, the quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Therefore, the correct answer is C. [tex]\(-8x^2 - 6x + 35\)[/tex].
1. Apply the Distributive Property:
The distributive property allows us to multiply each term in the first binomial by each term in the second binomial. It's also known as the FOIL method when dealing with two binomials: First, Outer, Inner, Last.
2. Multiply the First Terms:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
3. Multiply the Outer Terms:
[tex]\[
2x \cdot (-4x) = -8x^2
\][/tex]
4. Multiply the Inner Terms:
[tex]\[
5 \cdot 7 = 35
\][/tex]
5. Multiply the Last Terms:
[tex]\[
5 \cdot (-4x) = -20x
\][/tex]
6. Combine Like Terms:
- The terms involving [tex]\(x\)[/tex] are [tex]\(14x\)[/tex] and [tex]\(-20x\)[/tex]. Combine these to get:
[tex]\[
14x + (-20x) = -6x
\][/tex]
- The constant term remains as [tex]\(35\)[/tex].
7. Write the Final Expression:
By combining all our results, the quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Therefore, the correct answer is C. [tex]\(-8x^2 - 6x + 35\)[/tex].
