We appreciate your visit to Multiply the following expression tex x 2 5x 2x 2 x 3 tex Choose the correct option A tex 4x 4 9x 3 8x 2. 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 result of multiplying [tex]\((x^2 - 5x)\)[/tex] and [tex]\((2x^2 + x - 3)\)[/tex], we need to use the distributive property to expand the expression. Here's how you can do it step by step:
1. Distribute [tex]\(x^2\)[/tex]:
We first distribute [tex]\(x^2\)[/tex] to each term in the second polynomial:
[tex]\[
x^2 \cdot (2x^2 + x - 3) = 2x^4 + x^3 - 3x^2
\][/tex]
2. Distribute [tex]\(-5x\)[/tex]:
Next, distribute [tex]\(-5x\)[/tex] to each term in the second polynomial:
[tex]\[
-5x \cdot (2x^2 + x - 3) = -10x^3 - 5x^2 + 15x
\][/tex]
3. Combine all the terms:
Combine all the terms from the above results:
[tex]\[
2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x
\][/tex]
4. Simplify by combining like terms:
Group and combine the like terms to simplify:
- The [tex]\(x^4\)[/tex] term: [tex]\(2x^4\)[/tex]
- The [tex]\(x^3\)[/tex] terms: [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- The [tex]\(x\)[/tex] term: [tex]\(15x\)[/tex]
So, the final expanded and simplified expression is:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
Therefore, from the given options, the correct answer is:
B. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex]
1. Distribute [tex]\(x^2\)[/tex]:
We first distribute [tex]\(x^2\)[/tex] to each term in the second polynomial:
[tex]\[
x^2 \cdot (2x^2 + x - 3) = 2x^4 + x^3 - 3x^2
\][/tex]
2. Distribute [tex]\(-5x\)[/tex]:
Next, distribute [tex]\(-5x\)[/tex] to each term in the second polynomial:
[tex]\[
-5x \cdot (2x^2 + x - 3) = -10x^3 - 5x^2 + 15x
\][/tex]
3. Combine all the terms:
Combine all the terms from the above results:
[tex]\[
2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x
\][/tex]
4. Simplify by combining like terms:
Group and combine the like terms to simplify:
- The [tex]\(x^4\)[/tex] term: [tex]\(2x^4\)[/tex]
- The [tex]\(x^3\)[/tex] terms: [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- The [tex]\(x\)[/tex] term: [tex]\(15x\)[/tex]
So, the final expanded and simplified expression is:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
Therefore, from the given options, the correct answer is:
B. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex]
Thanks for taking the time to read Multiply the following expression tex x 2 5x 2x 2 x 3 tex Choose the correct option A tex 4x 4 9x 3 8x 2. 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
