Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Certainly! Here is the step-by-step process to add the given polynomials and represent the answer in standard form.
Given polynomials:
[tex]\[ \left(-4 y^3 - 5 y + 16\right) + \left(4 y^2 - y + 9\right) \][/tex]
To add these polynomials, we need to combine like terms. Like terms are terms that have the same variable raised to the same power.
### Step-by-Step Solution:
1. Identify and Arrange Like Terms:
- [tex]\( -4 y^3 \)[/tex] (from the first polynomial)
- [tex]\( 4 y^2 \)[/tex] (from the second polynomial)
- [tex]\( -5 y \)[/tex] (from the first polynomial)
- [tex]\( -y \)[/tex] (from the second polynomial)
- [tex]\( 16 \)[/tex] (from the first polynomial)
- [tex]\( 9 \)[/tex] (from the second polynomial)
2. Combine Like Terms:
- For [tex]\( y^3 \)[/tex] terms: There is only one term, [tex]\( -4 y^3 \)[/tex].
- For [tex]\( y^2 \)[/tex] terms: There is only one term, [tex]\( 4 y^2 \)[/tex].
- For [tex]\( y \)[/tex] terms:
[tex]\[ -5 y - y = -6 y \][/tex]
- For constant terms:
[tex]\[ 16 + 9 = 25 \][/tex]
3. Write the Combined Result:
- Combining all the like terms, we have:
[tex]\[ -4 y^3 + 4 y^2 - 6 y + 25 \][/tex]
### Final Answer in Expanded Form:
[tex]\[ \left(-4 y^3 - 5 y + 16\right) + \left(4 y^2 - y + 9\right) = -4 y^3 + 4 y^2 - 6 y + 25 \][/tex]
So, the expanded polynomial in standard form is:
[tex]\[ \boxed{-4y^3 + 4y^2 - 6y + 25} \][/tex]
Given polynomials:
[tex]\[ \left(-4 y^3 - 5 y + 16\right) + \left(4 y^2 - y + 9\right) \][/tex]
To add these polynomials, we need to combine like terms. Like terms are terms that have the same variable raised to the same power.
### Step-by-Step Solution:
1. Identify and Arrange Like Terms:
- [tex]\( -4 y^3 \)[/tex] (from the first polynomial)
- [tex]\( 4 y^2 \)[/tex] (from the second polynomial)
- [tex]\( -5 y \)[/tex] (from the first polynomial)
- [tex]\( -y \)[/tex] (from the second polynomial)
- [tex]\( 16 \)[/tex] (from the first polynomial)
- [tex]\( 9 \)[/tex] (from the second polynomial)
2. Combine Like Terms:
- For [tex]\( y^3 \)[/tex] terms: There is only one term, [tex]\( -4 y^3 \)[/tex].
- For [tex]\( y^2 \)[/tex] terms: There is only one term, [tex]\( 4 y^2 \)[/tex].
- For [tex]\( y \)[/tex] terms:
[tex]\[ -5 y - y = -6 y \][/tex]
- For constant terms:
[tex]\[ 16 + 9 = 25 \][/tex]
3. Write the Combined Result:
- Combining all the like terms, we have:
[tex]\[ -4 y^3 + 4 y^2 - 6 y + 25 \][/tex]
### Final Answer in Expanded Form:
[tex]\[ \left(-4 y^3 - 5 y + 16\right) + \left(4 y^2 - y + 9\right) = -4 y^3 + 4 y^2 - 6 y + 25 \][/tex]
So, the expanded polynomial in standard form is:
[tex]\[ \boxed{-4y^3 + 4y^2 - 6y + 25} \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.