We appreciate your visit to Which quadratic expression represents the product of these factors tex 2x 5 7 4x tex A tex 8x 2 6x 35 tex B tex 8x. 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], we can use the distributive property, often referred to as the FOIL method. FOIL stands for First, Outer, Inner, Last, which helps remember which terms to multiply.
Let's go through each step:
1. First: Multiply the first terms in each binomial:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
2. Outer: Multiply the outer terms in the product:
[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]
Now that we have multiplied the terms, let's combine them:
- Start with the quadratic term: [tex]\(-8x^2\)[/tex].
- Combine the linear terms: [tex]\(14x\)[/tex] (from the First) and [tex]\(-20x\)[/tex] (from the Last), which simplifies to:
[tex]\[
14x - 20x = -6x
\][/tex]
- Lastly, include the constant term: [tex]\(+35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
The expression that matches this calculation is option A: [tex]\(-8x^2 - 6x + 35\)[/tex].
Let's go through each step:
1. First: Multiply the first terms in each binomial:
[tex]\[
2x \cdot 7 = 14x
\][/tex]
2. Outer: Multiply the outer terms in the product:
[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]
Now that we have multiplied the terms, let's combine them:
- Start with the quadratic term: [tex]\(-8x^2\)[/tex].
- Combine the linear terms: [tex]\(14x\)[/tex] (from the First) and [tex]\(-20x\)[/tex] (from the Last), which simplifies to:
[tex]\[
14x - 20x = -6x
\][/tex]
- Lastly, include the constant term: [tex]\(+35\)[/tex].
Putting it all together, the quadratic expression is:
[tex]\[
-8x^2 - 6x + 35
\][/tex]
The expression that matches this calculation is option A: [tex]\(-8x^2 - 6x + 35\)[/tex].
Thanks for taking the time to read Which quadratic expression represents the product of these factors tex 2x 5 7 4x tex A tex 8x 2 6x 35 tex B tex 8x. 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
