A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

will medal for help Simplify: (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2

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

    let sin x= a and cos = b to make it look s easier :P \[\huge\rm (a-b)^2+(a+b)^2\] familiar wit the foil method ?

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

    ive heard of it before but I cant remember how it goes

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

    alright (a-b)^2 is same as (a-b)(a-b)|dw:1439569755635:dw| first multiply first term with the 2nd parentheses and then multiply 2nd term of 1st parentheses by 2nd one

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

    alright how would i apply that to this problem?

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

    so sin = a b= b (a-b)(a-b) apply the foil method \[\huge\rm \color{reD}{a}(a-b) \color{reD}{- b}(a-b)\] distribute

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

    I'm sorry im still confused? are we to plug in numbers or just the letters?

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

    well we don't have to i just change cos and sin with a b to make it a little bit easier

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

    oh okay I understand whats next?

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

    (a-b)(a-b) apply the foil method \[\huge\rm \color{reD}{a}(a-b) \color{reD}{- b}(a-b)\] distribute (a-b) by a and then (a-b) by -b

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

    |dw:1439570120307:dw| multiply both terms by a a times a - a times b = ?

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

    a^2 - b times a?

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

    yes right -b(a-b) =?

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

    ot would it just be (a-b)^2

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

    no

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

    \(\color{blue}{\text{Originally Posted by}}\) @macim a^2 - b times a? \(\color{blue}{\text{End of Quote}}\) this is right for first part

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

    oh alright! and then it would be a times b -b^2?

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

    well it is -b(a-b) signs!!!

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

    -b times a = ?

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

    wouldn't it just equal -b times a because you cant multiply those variables?

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

    yes negative ab -ab so -b times -b = ??

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

    -2b?

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

    no b times b is b^2 is right but there is sign mistake negative times negative = ?

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

    oh right sorry it would just be 2b

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

    or b^2

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

    yes right

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

    the b^2 is right or 2b?

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

    b^2 when you multiply same bases you should add their exponents

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

    now write it together|dw:1439570550698:dw| \[\huge\rm a^2-ab-ab+b^2\] combine like terms

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

    would you just end up with a^2+b^2

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

    -ab-ab=??

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

    i thought they would just cancel each other out. but if they don't wouldn't it be ab^2

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

    no both terms are same and same sign so you can't** cancel them \[\rm a-a= 0~~~-a-a=-2a\] when you add or subtract like terms just simply add or subtract their coefficients and when you multiply same bases then you should add their exponents \[\rm x^1 \times x^1= x^{1+1}\]

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

    -ab-ab is same as \[\huge\rm \color{red}{-1}ab\color{red}{-1}ab=(-1-1)ab\]

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

    alright i understand that

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

    so it's equal to -2ab ? right or no?

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

    yes?

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

    i'm asking yes or no ?

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

    yes

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

    -ab-ab is same as \[\huge\rm \color{red}{-1}ab\color{red}{-1}ab=(-1-1)ab=-2ab\]

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

    so \[\huge\rm (a-b)^2=a^2-2ab+b^2\] now 2nd part of the question (a+b)^2 which is same as (a+b)(a+b) foil it!

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

    foil (a-b)^2=a^2-2ab+b^2?

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

    yea that's for (a-b)^2 now foil (a+b)^2

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

    I'm sorry I really don't understand?

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

    like i said (a+b)^2 is same as (a+b)(a+b) now just multiply like we did for (a-b)^2

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

    or in other words square of first number and square of 2nd number and multiply both terms by 2 here is an example |dw:1439571636107:dw| just like this

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

    would it just be a^2+b^2

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

    no llook at the drawing ^^^^

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

    a^2+2b^2+2?

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

    |dw:1439571972434:dw| there should be 3 terms

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

    so would I have to make up another because we only have 2

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

    well you don't make up you need to know how to foil method works let's try box method to foil binomial |dw:1439572122692:dw| write one parentheses at the top of the box and one left side now start multiplying terms

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

    so a^2+b^2+ab+2b

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

    how did you get 2b ?

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

    because of b times b

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

    but that would b^2 wouldn't it

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

    yes right so how did you get 2b ?

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

    |dw:1439572443606:dw| now multiply a+b by b and write it down in the box

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

    |dw:1439572494627:dw|