Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Let's delve into the given polynomial multiplication step-by-step to deduce the correct product:
We have two polynomials:
[tex]\[ (2y - 3) \][/tex]
and
[tex]\[ (3y^2 + 4y - 5) \][/tex]
We need to find the product of these two polynomials.
Step-by-Step Calculation:
1. Distribute each term of the first polynomial with each term of the second polynomial:
2. Multiply [tex]\(2y\)[/tex] with each term in [tex]\(3y^2 + 4y - 5\)[/tex]:
[tex]\[ 2y \cdot 3y^2 = 6y^3 \][/tex]
[tex]\[ 2y \cdot 4y = 8y^2 \][/tex]
[tex]\[ 2y \cdot (-5) = -10y \][/tex]
3. Multiply [tex]\(-3\)[/tex] with each term in [tex]\(3y^2 + 4y - 5\)[/tex]:
[tex]\[ -3 \cdot 3y^2 = -9y^2 \][/tex]
[tex]\[ -3 \cdot 4y = -12y \][/tex]
[tex]\[ -3 \cdot (-5) = 15 \][/tex]
Now, add all these individual products together:
[tex]\[ 6y^3 + 8y^2 - 10y - 9y^2 - 12y + 15 \][/tex]
4. Combine like terms:
[tex]\[ 6y^3 + (8y^2 - 9y^2) + (-10y - 12y) + 15 \][/tex]
[tex]\[ 6y^3 - y^2 - 22y + 15 \][/tex]
Therefore, the polynomial resulting from multiplying [tex]\((2y - 3)\)[/tex] and [tex]\((3y^2 + 4y - 5)\)[/tex] is:
[tex]\[ \boxed{6y^3 - y^2 - 22y + 15} \][/tex]
Looking at the given options, the correct match for this polynomial is:
[tex]\[ 6y^3 - y^2 - 22y + 15 \][/tex]
So, the correct polynomial product is:
[tex]\[ \boxed{6y^3 - y^2 - 22y + 15} \][/tex]
from the given answer options list, which corresponds to none of the directly given choices because there's a typo in the provided answers.
We have two polynomials:
[tex]\[ (2y - 3) \][/tex]
and
[tex]\[ (3y^2 + 4y - 5) \][/tex]
We need to find the product of these two polynomials.
Step-by-Step Calculation:
1. Distribute each term of the first polynomial with each term of the second polynomial:
2. Multiply [tex]\(2y\)[/tex] with each term in [tex]\(3y^2 + 4y - 5\)[/tex]:
[tex]\[ 2y \cdot 3y^2 = 6y^3 \][/tex]
[tex]\[ 2y \cdot 4y = 8y^2 \][/tex]
[tex]\[ 2y \cdot (-5) = -10y \][/tex]
3. Multiply [tex]\(-3\)[/tex] with each term in [tex]\(3y^2 + 4y - 5\)[/tex]:
[tex]\[ -3 \cdot 3y^2 = -9y^2 \][/tex]
[tex]\[ -3 \cdot 4y = -12y \][/tex]
[tex]\[ -3 \cdot (-5) = 15 \][/tex]
Now, add all these individual products together:
[tex]\[ 6y^3 + 8y^2 - 10y - 9y^2 - 12y + 15 \][/tex]
4. Combine like terms:
[tex]\[ 6y^3 + (8y^2 - 9y^2) + (-10y - 12y) + 15 \][/tex]
[tex]\[ 6y^3 - y^2 - 22y + 15 \][/tex]
Therefore, the polynomial resulting from multiplying [tex]\((2y - 3)\)[/tex] and [tex]\((3y^2 + 4y - 5)\)[/tex] is:
[tex]\[ \boxed{6y^3 - y^2 - 22y + 15} \][/tex]
Looking at the given options, the correct match for this polynomial is:
[tex]\[ 6y^3 - y^2 - 22y + 15 \][/tex]
So, the correct polynomial product is:
[tex]\[ \boxed{6y^3 - y^2 - 22y + 15} \][/tex]
from the given answer options list, which corresponds to none of the directly given choices because there's a typo in the provided answers.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.