Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

danielcb114

  • one year ago

How to factor y^4+1/2+1/(16y^4)? I know that it factors into (y^2+1/(4y^2))^2, but I can't figure out why. I need to simplify this for an arc length integral. Any help is greatly appreciated.

  • This Question is Closed
  1. danielcb114
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It is copied correctly; a 3 term sum.

  2. radar
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Have you copies it correctly or is Y^4 + (1/2) (y^2) + (1/16)(6^4)?

  3. radar
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Does the middle term have the variable y^2 in it?

  4. danielcb114
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Unfortunately, no. I have checked my algebra up to that point and I'm also looking at a solution manual; which skips the factoring step. I haven't seen anything like it before. I'm thinking something similar to completing the square is the way to go, but I'm lost at this point. Thanks for your help, by the way.:)

  5. radar
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    O.K. I was thinking of a perfect square, but now I see that I was on the wrong track.

  6. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    there is a typo in your question somewhere for sure

  7. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ y^2+\frac{1}{4}y^2=\frac{5}{4}y^2\] once you combine like terms

  8. danielcb114
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry, I just noticed it in the second part. The original question is correct, but the term should be squared.

  9. danielcb114
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I have since corrected it; thank you.

  10. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    still a typo, since \((\frac{5}{4}y^2)^2=\frac{25}{16}y^4\)

  11. danielcb114
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry again; I didn't see the missing parentheses. Now it is corrected(knock on wood);)

  12. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oooh now i get it \[\left(y^2+\frac{1}{4y^2}\right)^2\]

  13. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    happy holidaze! you done?

  14. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[y^4+\frac{1}{2}+\frac{1}{16y^4} \] \[(y^2)^2+2 y^2 \frac{1}{4y^2}+(\frac{1}{4y^2})^2\] This is in the form \[a^2+2ab+b^2 \] which can be factored into the form: \[(a+b)^2 \]

  15. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    probably easiest to see if you multiply out and see that it works

  16. danielcb114
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ahh, yes; I don't know why I didn't see that before. I wanted to express it that way, but for some reason my mind turned off the possibility. Thank you, myininaya, satellite73 and radar. You've made me very happy!

  17. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw (from all of us)

  18. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I hope you all have a great happy holiday! :)

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.