# Factoring algebraic complex expression

Maxo

## Homework Statement

Factor the expression ac-bd+adi+bci

## 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?

## Answers and Replies

Fightfish
The common factor in the remaing terms is b, and if we also factor out b we get
a(c+di)-b(d-ci)
Do you realise the similarity between the factors (c+di) and (d-ci)? How can you make them the same?

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Maxo
Do you realise the similarity between the factors (c+di) and (d-ci)? How can you make them the same?
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?

Fightfish
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

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Gold Member
For your second step, factor out bi instead of just b. Be more careful with signs and brackets.

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Maxo
Now I see it :)

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