Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To find the product of the binomials [tex]\(\left(-2d^2 + s\right)\left(5d^2 - 6s\right)\)[/tex], we can use the distributive property (also known as the FOIL method for binomials). Let’s go through the steps:
1. First terms: Multiply the first terms in each binomial: [tex]\(-2d^2 \cdot 5d^2\)[/tex].
[tex]\[ -2d^2 \cdot 5d^2 = -10d^4 \][/tex]
2. Outer terms: Multiply the outer terms in each binomial: [tex]\(-2d^2 \cdot -6s\)[/tex].
[tex]\[ -2d^2 \cdot -6s = 12d^2s \][/tex]
3. Inner terms: Multiply the inner terms in each binomial: [tex]\(s \cdot 5d^2\)[/tex].
[tex]\[ s \cdot 5d^2 = 5d^2s \][/tex]
4. Last terms: Multiply the last terms in each binomial: [tex]\(s \cdot -6s\)[/tex].
[tex]\[ s \cdot -6s = -6s^2 \][/tex]
Now, add all these products together:
[tex]\[ -10d^4 + 12d^2s + 5d^2s - 6s^2 \][/tex]
Combine the like terms ([tex]\(12d^2s\)[/tex] and [tex]\(5d^2s\)[/tex]):
[tex]\[ -10d^4 + (12d^2s + 5d^2s) - 6s^2 \][/tex]
[tex]\[ -10d^4 + 17d^2s - 6s^2 \][/tex]
So, the product of [tex]\(\left(-2d^2 + s\right) \left(5d^2 - 6s\right)\)[/tex] is:
[tex]\[ \boxed{-10d^4 + 17d^2s - 6s^2} \][/tex]
Therefore, the correct answer is:
[tex]\[ -10 d^4 + 17 d^2 s - 6 s^2 \][/tex]
1. First terms: Multiply the first terms in each binomial: [tex]\(-2d^2 \cdot 5d^2\)[/tex].
[tex]\[ -2d^2 \cdot 5d^2 = -10d^4 \][/tex]
2. Outer terms: Multiply the outer terms in each binomial: [tex]\(-2d^2 \cdot -6s\)[/tex].
[tex]\[ -2d^2 \cdot -6s = 12d^2s \][/tex]
3. Inner terms: Multiply the inner terms in each binomial: [tex]\(s \cdot 5d^2\)[/tex].
[tex]\[ s \cdot 5d^2 = 5d^2s \][/tex]
4. Last terms: Multiply the last terms in each binomial: [tex]\(s \cdot -6s\)[/tex].
[tex]\[ s \cdot -6s = -6s^2 \][/tex]
Now, add all these products together:
[tex]\[ -10d^4 + 12d^2s + 5d^2s - 6s^2 \][/tex]
Combine the like terms ([tex]\(12d^2s\)[/tex] and [tex]\(5d^2s\)[/tex]):
[tex]\[ -10d^4 + (12d^2s + 5d^2s) - 6s^2 \][/tex]
[tex]\[ -10d^4 + 17d^2s - 6s^2 \][/tex]
So, the product of [tex]\(\left(-2d^2 + s\right) \left(5d^2 - 6s\right)\)[/tex] is:
[tex]\[ \boxed{-10d^4 + 17d^2s - 6s^2} \][/tex]
Therefore, the correct answer is:
[tex]\[ -10 d^4 + 17 d^2 s - 6 s^2 \][/tex]
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, your go-to source for reliable answers. Come back soon for more expert insights.