Problem #DES-algebraictricks

Problem

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.