Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Certainly! Let's go through the process of adding the two given polynomials step by step.
We are given two polynomials:
[tex]\[ (8r^2 - 7r - 9) \][/tex]
and
[tex]\[ (-r^2 + r). \][/tex]
### Step-by-Step Solution
1. Identify the like terms:
- The first polynomial: [tex]\(8r^2 - 7r - 9\)[/tex]
- The second polynomial: [tex]\(-r^2 + r\)[/tex]
2. Group the like terms together:
- For [tex]\(r^2\)[/tex] terms: [tex]\(8r^2\)[/tex] from the first polynomial and [tex]\(-r^2\)[/tex] from the second polynomial.
- For [tex]\(r\)[/tex] terms: [tex]\(-7r\)[/tex] from the first polynomial and [tex]\(+r\)[/tex] from the second polynomial.
- For the constant term: [tex]\(-9\)[/tex] from the first polynomial (the second polynomial does not have a constant term).
3. Add the coefficients of the like terms:
- [tex]\(r^2\)[/tex] term: [tex]\(8r^2 + (-r^2) = 8r^2 - r^2 = 7r^2\)[/tex]
- [tex]\(r\)[/tex] term: [tex]\(-7r + r = -7r + r = -6r\)[/tex]
- Constant term: [tex]\(-9 + 0 = -9\)[/tex]
4. Combine the results:
- The expanded polynomial in standard form will be: [tex]\( 7r^2 - 6r - 9 \)[/tex]
Therefore, the final answer is:
[tex]\[ (8r^2 - 7r - 9) + (-r^2 + r) = 7r^2 - 6r - 9 \][/tex]
We are given two polynomials:
[tex]\[ (8r^2 - 7r - 9) \][/tex]
and
[tex]\[ (-r^2 + r). \][/tex]
### Step-by-Step Solution
1. Identify the like terms:
- The first polynomial: [tex]\(8r^2 - 7r - 9\)[/tex]
- The second polynomial: [tex]\(-r^2 + r\)[/tex]
2. Group the like terms together:
- For [tex]\(r^2\)[/tex] terms: [tex]\(8r^2\)[/tex] from the first polynomial and [tex]\(-r^2\)[/tex] from the second polynomial.
- For [tex]\(r\)[/tex] terms: [tex]\(-7r\)[/tex] from the first polynomial and [tex]\(+r\)[/tex] from the second polynomial.
- For the constant term: [tex]\(-9\)[/tex] from the first polynomial (the second polynomial does not have a constant term).
3. Add the coefficients of the like terms:
- [tex]\(r^2\)[/tex] term: [tex]\(8r^2 + (-r^2) = 8r^2 - r^2 = 7r^2\)[/tex]
- [tex]\(r\)[/tex] term: [tex]\(-7r + r = -7r + r = -6r\)[/tex]
- Constant term: [tex]\(-9 + 0 = -9\)[/tex]
4. Combine the results:
- The expanded polynomial in standard form will be: [tex]\( 7r^2 - 6r - 9 \)[/tex]
Therefore, the final answer is:
[tex]\[ (8r^2 - 7r - 9) + (-r^2 + r) = 7r^2 - 6r - 9 \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.