We appreciate your visit to Select the correct answer Which quadratic expression represents the product of these factors tex 2x 5 7 4x tex A tex 8x 2 34x 35. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], follow these steps:
### Step 1: Apply the Distributive Property
We need to multiply each term in the first binomial by each term in the second binomial. This is also known as the FOIL method, which stands for First, Outer, Inner, and Last.
### Step 2: Multiply the Terms
Let's break down the multiplication:
1. First: Multiply the first terms in each binomial:
[tex]\[
(2x) \cdot (7) = 14x
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
(2x) \cdot (-4x) = -8x^2
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
(5) \cdot (7) = 35
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
(5) \cdot (-4x) = -20x
\][/tex]
### Step 3: Combine Like Terms
Now, add all these products together:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
### Step 4: Simplify the Expression
Combine the [tex]\(x\)[/tex]-terms:
[tex]\[
-8x^2 + (14x - 20x) + 35
\][/tex]
[tex]\[
-8x^2 - 6x + 35
\][/tex]
### Conclusion
The quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Given this, the correct answer is:
C. [tex]\(-8x^2 - 6x + 35\)[/tex]
### Step 1: Apply the Distributive Property
We need to multiply each term in the first binomial by each term in the second binomial. This is also known as the FOIL method, which stands for First, Outer, Inner, and Last.
### Step 2: Multiply the Terms
Let's break down the multiplication:
1. First: Multiply the first terms in each binomial:
[tex]\[
(2x) \cdot (7) = 14x
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
(2x) \cdot (-4x) = -8x^2
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
(5) \cdot (7) = 35
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
(5) \cdot (-4x) = -20x
\][/tex]
### Step 3: Combine Like Terms
Now, add all these products together:
[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]
### Step 4: Simplify the Expression
Combine the [tex]\(x\)[/tex]-terms:
[tex]\[
-8x^2 + (14x - 20x) + 35
\][/tex]
[tex]\[
-8x^2 - 6x + 35
\][/tex]
### Conclusion
The quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
Given this, the correct answer is:
C. [tex]\(-8x^2 - 6x + 35\)[/tex]
Thanks for taking the time to read Select the correct answer Which quadratic expression represents the product of these factors tex 2x 5 7 4x tex A tex 8x 2 34x 35. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
