We appreciate your visit to Simplify tex left 5x 2 9x 6 right 4x 8 tex A tex 20x 3 4x 2 48x 48 tex B tex 20x 3 76x. 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 simplify the expression [tex]\((5x^2 + 9x + 6)(4x - 8)\)[/tex], we need to multiply each term in the first polynomial by each term in the second polynomial. Let's go through this step-by-step:
1. Distribute [tex]\(4x\)[/tex] Across [tex]\((5x^2 + 9x + 6)\)[/tex]:
- Multiply [tex]\(5x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
5x^2 \times 4x = 20x^3
\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x \times 4x = 36x^2
\][/tex]
- Multiply [tex]\(6\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
6 \times 4x = 24x
\][/tex]
After this step, we have [tex]\(20x^3 + 36x^2 + 24x\)[/tex].
2. Distribute [tex]\(-8\)[/tex] Across [tex]\((5x^2 + 9x + 6)\)[/tex]:
- Multiply [tex]\(5x^2\)[/tex] by [tex]\(-8\)[/tex]:
[tex]\[
5x^2 \times -8 = -40x^2
\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(-8\)[/tex]:
[tex]\[
9x \times -8 = -72x
\][/tex]
- Multiply [tex]\(6\)[/tex] by [tex]\(-8\)[/tex]:
[tex]\[
6 \times -8 = -48
\][/tex]
After this step, we have [tex]\(-40x^2 - 72x - 48\)[/tex].
3. Combine Like Terms:
- Combine [tex]\(x^3\)[/tex] terms:
[tex]\[
20x^3
\][/tex]
- Combine [tex]\(x^2\)[/tex] terms:
[tex]\[
36x^2 - 40x^2 = -4x^2
\][/tex]
- Combine [tex]\(x\)[/tex] terms:
[tex]\[
24x - 72x = -48x
\][/tex]
- Constant term:
[tex]\[
-48
\][/tex]
The simplified expression is [tex]\(20x^3 - 4x^2 - 48x - 48\)[/tex].
So, the correct option is D: [tex]\(20x^3 - 4x^2 - 48x - 48\)[/tex].
1. Distribute [tex]\(4x\)[/tex] Across [tex]\((5x^2 + 9x + 6)\)[/tex]:
- Multiply [tex]\(5x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
5x^2 \times 4x = 20x^3
\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
9x \times 4x = 36x^2
\][/tex]
- Multiply [tex]\(6\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
6 \times 4x = 24x
\][/tex]
After this step, we have [tex]\(20x^3 + 36x^2 + 24x\)[/tex].
2. Distribute [tex]\(-8\)[/tex] Across [tex]\((5x^2 + 9x + 6)\)[/tex]:
- Multiply [tex]\(5x^2\)[/tex] by [tex]\(-8\)[/tex]:
[tex]\[
5x^2 \times -8 = -40x^2
\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(-8\)[/tex]:
[tex]\[
9x \times -8 = -72x
\][/tex]
- Multiply [tex]\(6\)[/tex] by [tex]\(-8\)[/tex]:
[tex]\[
6 \times -8 = -48
\][/tex]
After this step, we have [tex]\(-40x^2 - 72x - 48\)[/tex].
3. Combine Like Terms:
- Combine [tex]\(x^3\)[/tex] terms:
[tex]\[
20x^3
\][/tex]
- Combine [tex]\(x^2\)[/tex] terms:
[tex]\[
36x^2 - 40x^2 = -4x^2
\][/tex]
- Combine [tex]\(x\)[/tex] terms:
[tex]\[
24x - 72x = -48x
\][/tex]
- Constant term:
[tex]\[
-48
\][/tex]
The simplified expression is [tex]\(20x^3 - 4x^2 - 48x - 48\)[/tex].
So, the correct option is D: [tex]\(20x^3 - 4x^2 - 48x - 48\)[/tex].
Thanks for taking the time to read Simplify tex left 5x 2 9x 6 right 4x 8 tex A tex 20x 3 4x 2 48x 48 tex B tex 20x 3 76x. 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
