General comments on Algebra
At A-level and IB you generally have to go further without guidance to get a result than at GCSE. Unfortunately if you make a mistake you often don't get the result you are looking for at all, so you get stuck and abandon the problem.
The only answer is to be very careful at each step that you get the signs right, put all the brackets in the right places, and so on. Don't be tempted to leave bits out to save writing, it is worth writing out every step if it helps you avoid mistakes.
Be alert for standard forms: e.g. a2-b2=(a+b)(a-b) which is often very helpful.
In complex analysis there is another form of this: a2+b2=(a+ib)(a-ib)
Look out for quadratics, in any form that they may arise: the terms may be on opposite sides of the = sign. Something like ax+b+c/x=0 is also a quadratic - you just have to multiply both sides by x.
This is also a quadratic - in x2: ax4+bx2+c=0
You can still use the formula, but this time it will be x2=-b etc.
A quadratic is a friend - when you see it you know you can apply the formula.