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Factoring algebraic complex expression

  1. Jul 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Factor the expression ac-bd+adi+bci

    2. Relevant equations


    3. The attempt at a solution
    We can factor the variable 'a' which gives:
    a(c+di)-bd+bci
    The common factor in the remaing terms is b, and if we also factor out b we get
    a(c+di)-b(d+ci)

    But this is not the way I want it factorized. I want it to be factored completely. How can that be done step by step?
     
  2. jcsd
  3. Jul 23, 2014 #2
    Do you realise the similarity between the factors (c+di) and (d-ci)? How can you make them the same?
     
    Last edited: Jul 23, 2014
  4. Jul 23, 2014 #3
    I made a misstake, it should be a(c+di)-b(d-ci). Anyway so you're saying (c+di) and (d-ci) can be made the same. I actually don't see how that could be done? I mean both the real and the imaginary parts of these expressions are different. How are they the same?
     
  5. Jul 23, 2014 #4
    Maybe I wasn't very clear with what I meant by "make the same", but what I was trying to convey is identifying the common factor between these two terms. Notice that they differ by a factor of i
     
  6. Jul 23, 2014 #5
    For your second step, factor out bi instead of just b. Be more careful with signs and brackets.
     
  7. Jul 23, 2014 #6
    Now I see it :)

    Is there some rule (algorithm) / procedure to follow when factoring like this?
     
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