Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Cutiepo0

explain how you can use the pattern for expanding a binomial to expand (x+y+z)^10

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 2

    This is going to be long a messy in practice although simple in theory. Consider first (x + (y+z) )^10. This is a binomial in x and (y+z). Expand this using standard binomial theory. Then you will need to expand all of the (y+z)^j terms.

    • 2 years ago
  2. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 2

    To work a smaller example, consider (x+y+z)^3. Write this as (x + (y+z) )^3. By the binomial theorem this is equal to x^3 + 3x^2(y+z) + 3x(y+z)^2 + (y+z)^3 Now expand the (y+z) terms x^3 + 3x^2y + 3x^2z + 3xy^2 + 6xyz + 3xz^2 + y^3 + 3y^2z + 3yz^2 + z^3

    • 2 years ago
  3. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 0

    I would just use the multinomial expansion

    • 2 years ago
  4. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 2

    That too. Either way, it's going to be tedious calculation.

    • 2 years ago
  5. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 2

    although perhaps it would result in a slightly neater arrangement of terms. x^3 + y^3 + z^3 + 3(x^2y + y^2z + z^2x + x^2z + y^2x + z^2y) + 6xyz

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.