Problem: Quadratic identities

Problem

Using \(\left( a+b \right)\left( c+d \right)=ac+ad+bc+bd\)

1. Prove that \(\left( a+b \right)\left( a-b \right)=a^2-b^2\)
2. Prove that \({\left( a+b \right)}^2=a^2+2ab+b^2\)
3. Prove that \({\left( a-b \right)}^2=a^2-2ab+b^2\)