Question

If ab = 8 and a^2+b^2=16, then what is the value of (a+b)^2?

Answer 1

Note that (a+b)^2 = a^2 + 2ab + b^2.  This is always true.

Let's re-write the given "ab = 8 and a^2+b^2=16" as
  a^2 + 2ab + b^2 = 16 + 2ab, or, equivalently, as 
       (a+b)^2          = 16 + 2(8) = 32. 
 This is the answer we wanted.