We appreciate your visit to Choose the product of tex left 3x 2 7 right left 6x 2 4x 5 right tex A tex 63x 2 28x 35 tex B. 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 :
Let's find the product of the two polynomials [tex]\((3x^2 + 7)(6x^2 - 4x + 5)\)[/tex].
1. Distribute the terms from the first polynomial:
- First, distribute [tex]\(3x^2\)[/tex] to each term in the second polynomial:
- [tex]\(3x^2 \cdot 6x^2 = 18x^4\)[/tex]
- [tex]\(3x^2 \cdot (-4x) = -12x^3\)[/tex]
- [tex]\(3x^2 \cdot 5 = 15x^2\)[/tex]
Now we have:
[tex]\[
18x^4 - 12x^3 + 15x^2
\][/tex]
2. Distribute the second term from the first polynomial, 7, to each term in the second polynomial:
- [tex]\(7 \cdot 6x^2 = 42x^2\)[/tex]
- [tex]\(7 \cdot (-4x) = -28x\)[/tex]
- [tex]\(7 \cdot 5 = 35\)[/tex]
Now we have:
[tex]\[
42x^2 - 28x + 35
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(15x^2 + 42x^2 = 57x^2\)[/tex]
4. Write the final expression:
The full polynomial expression is:
[tex]\[
18x^4 - 12x^3 + 57x^2 - 28x + 35
\][/tex]
After performing these steps, we can see that the correct answer is [tex]\(\boxed{18x^4 - 12x^3 + 57x^2 - 28x + 35}\)[/tex], which corresponds to option D.
1. Distribute the terms from the first polynomial:
- First, distribute [tex]\(3x^2\)[/tex] to each term in the second polynomial:
- [tex]\(3x^2 \cdot 6x^2 = 18x^4\)[/tex]
- [tex]\(3x^2 \cdot (-4x) = -12x^3\)[/tex]
- [tex]\(3x^2 \cdot 5 = 15x^2\)[/tex]
Now we have:
[tex]\[
18x^4 - 12x^3 + 15x^2
\][/tex]
2. Distribute the second term from the first polynomial, 7, to each term in the second polynomial:
- [tex]\(7 \cdot 6x^2 = 42x^2\)[/tex]
- [tex]\(7 \cdot (-4x) = -28x\)[/tex]
- [tex]\(7 \cdot 5 = 35\)[/tex]
Now we have:
[tex]\[
42x^2 - 28x + 35
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(15x^2 + 42x^2 = 57x^2\)[/tex]
4. Write the final expression:
The full polynomial expression is:
[tex]\[
18x^4 - 12x^3 + 57x^2 - 28x + 35
\][/tex]
After performing these steps, we can see that the correct answer is [tex]\(\boxed{18x^4 - 12x^3 + 57x^2 - 28x + 35}\)[/tex], which corresponds to option D.
Thanks for taking the time to read Choose the product of tex left 3x 2 7 right left 6x 2 4x 5 right tex A tex 63x 2 28x 35 tex B. 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
