1. What is the most common mistake people make when expanding brackets?
Most teachers will tell you that students forget to change all of the signs inside the bracket when expanding by a negative number. e.g. -3(x − 2) = -3x + 6 (common mistake is to put -3x − 6)
2. Which is the best method for expanding two brackets (quadratics)?
Whichever one works for you! Obviously the quickest way, providing you are accurate, is to do it in your head. Otherwise methods such as the FOIL method are all satisfactory.
3. Why is (x + 2)2 not equal to x2 + 4 ?
Because the power of two is telling you to multipy the bracket by itself
i.e. (x + 2)2 = (x + 2)(x + 2) = x2+ 4x + 4