Today we will solve some problems using algebraic tricks, mostly
related to turning a sum into a product or using an identity involving
squares.
The ones particularly useful are: \((a+b)^2 =
a^2 +b^2 +2ab\), \((a-b)^2 = a^2 +b^2
-2ab\) and \((a-b) \times (a+b) = a^2
-b^2\). While we are at squares, it is also worth noting that any
square of a real number is never a negative number.